├── .github └── workflows │ └── general.yaml ├── .gitignore ├── Cargo.toml ├── LICENSE ├── README.md ├── benches ├── Figures │ ├── proofSizes.pdf │ └── proverVerifierTimes.pdf ├── elgamal-plot.txt ├── elgamal.rs ├── kzg_elgamal.rs ├── kzg_paillier.rs ├── ourPlots.ipynb ├── paillier-plot.txt ├── plots.py └── range_proof.rs ├── contracts ├── BN254.sol ├── Constants.sol ├── FDE.sol ├── FDEPaillier.sol ├── LibUint1024.sol └── Types.sol └── src ├── adaptor_sig.rs ├── commit ├── kzg.rs └── mod.rs ├── dleq.rs ├── encrypt ├── elgamal │ ├── mod.rs │ ├── split_scalar.rs │ └── utils.rs └── mod.rs ├── hash.rs ├── lib.rs ├── range_proof ├── mod.rs ├── poly.rs └── utils.rs ├── tests └── mod.rs └── veck ├── kzg ├── elgamal │ ├── encryption.rs │ └── mod.rs ├── mod.rs └── paillier │ ├── encrypt.rs │ ├── mod.rs │ ├── random.rs │ ├── server.rs │ └── utils.rs └── mod.rs /.github/workflows/general.yaml: -------------------------------------------------------------------------------- 1 | name: general code check 2 | 3 | on: 4 | push: 5 | branches: [main] 6 | pull_request: 7 | 8 | jobs: 9 | test: 10 | name: test 11 | runs-on: ubuntu-latest 12 | steps: 13 | - uses: actions/checkout@v4 14 | - uses: dtolnay/rust-toolchain@stable 15 | - name: Run tests 16 | run: cargo test --release --features parallel 17 | fmt: 18 | name: fmt 19 | runs-on: ubuntu-latest 20 | env: 21 | RUSTFLAGS: -Dwarnings # fails on warnings as well 22 | steps: 23 | - uses: actions/checkout@v4 24 | - uses: dtolnay/rust-toolchain@stable 25 | with: 26 | components: rustfmt 27 | - name: enforce formatting 28 | run: cargo fmt --check 29 | 30 | clippy: 31 | name: clippy 32 | runs-on: ubuntu-latest 33 | env: 34 | RUSTFLAGS: -Dwarnings # fails on warnings as well 35 | steps: 36 | - uses: actions/checkout@v4 37 | - uses: dtolnay/rust-toolchain@stable 38 | with: 39 | components: clippy 40 | - name: linting 41 | run: cargo clippy --tests --examples --all-features 42 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | /target 2 | /Cargo.lock 3 | -------------------------------------------------------------------------------- /Cargo.toml: -------------------------------------------------------------------------------- 1 | [package] 2 | name = "fde" 3 | version = "0.1.0" 4 | edition = "2021" 5 | 6 | [profile.dev] 7 | opt-level = 3 8 | 9 | [features] 10 | default = ["std", "parallel"] 11 | std = [ 12 | "ark-crypto-primitives/std", 13 | "ark-ec/std", 14 | "ark-ff/std", 15 | "ark-poly/std", 16 | "ark-poly-commit/std", 17 | "ark-serialize/std", 18 | "ark-std/std", 19 | ] 20 | parallel = [ 21 | "ark-crypto-primitives/parallel", 22 | "ark-ec/parallel", 23 | "ark-ff/parallel", 24 | "ark-poly/parallel", 25 | "ark-poly-commit/parallel", 26 | "ark-std/parallel", 27 | "rayon" 28 | ] 29 | 30 | [dependencies] 31 | ark-crypto-primitives = { version = "0.4", default-features = false, features = ["signature"] } 32 | ark-ec = { version = "0.4", default-features = false } 33 | ark-ff = { version = "0.4", default-features = false } 34 | ark-poly = { version = "0.4", default-features = false } 35 | ark-poly-commit = { version = "0.4", default-features = false } 36 | ark-serialize = { version = "0.4", default-features = false } 37 | ark-std = { version = "0.4", default-features = false } 38 | num-bigint = { version = "0.4", features = ["rand"] } 39 | num-integer = "0.1" 40 | num-prime = "0.4" 41 | digest = { version = "0.10", default-features = false } 42 | rayon = { version = "1.8", optional = true } 43 | thiserror = "1" 44 | 45 | [dev-dependencies] 46 | ark-bls12-381 = "0.4" 47 | ark-secp256k1 = "0.4" 48 | criterion = "0.5" 49 | sha3 = "0.10" 50 | 51 | [[bench]] 52 | name = "kzg-paillier-veck" 53 | path = "benches/kzg_paillier.rs" 54 | harness = false 55 | 56 | [[bench]] 57 | name = "kzg-elgamal-veck" 58 | path = "benches/kzg_elgamal.rs" 59 | harness = false 60 | 61 | [[bench]] 62 | name = "split-elgamal-encryption" 63 | path = "benches/elgamal.rs" 64 | harness = false 65 | 66 | [[bench]] 67 | name = "range-proof" 68 | path = "benches/range_proof.rs" 69 | harness = false 70 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU AFFERO GENERAL PUBLIC LICENSE 2 | Version 3, 19 November 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU Affero General Public License is a free, copyleft license for 11 | software and other kinds of works, specifically designed to ensure 12 | cooperation with the community in the case of network server software. 13 | 14 | The licenses for most software and other practical works are designed 15 | to take away your freedom to share and change the works. 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It is safest 628 | to attach them to the start of each source file to most effectively 629 | state the exclusion of warranty; and each file should have at least 630 | the "copyright" line and a pointer to where the full notice is found. 631 | 632 | 633 | Copyright (C) 634 | 635 | This program is free software: you can redistribute it and/or modify 636 | it under the terms of the GNU Affero General Public License as published 637 | by the Free Software Foundation, either version 3 of the License, or 638 | (at your option) any later version. 639 | 640 | This program is distributed in the hope that it will be useful, 641 | but WITHOUT ANY WARRANTY; without even the implied warranty of 642 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 643 | GNU Affero General Public License for more details. 644 | 645 | You should have received a copy of the GNU Affero General Public License 646 | along with this program. If not, see . 647 | 648 | Also add information on how to contact you by electronic and paper mail. 649 | 650 | If your software can interact with users remotely through a computer 651 | network, you should also make sure that it provides a way for users to 652 | get its source. For example, if your program is a web application, its 653 | interface could display a "Source" link that leads users to an archive 654 | of the code. There are many ways you could offer source, and different 655 | solutions will be better for different programs; see section 13 for the 656 | specific requirements. 657 | 658 | You should also get your employer (if you work as a programmer) or school, 659 | if any, to sign a "copyright disclaimer" for the program, if necessary. 660 | For more information on this, and how to apply and follow the GNU AGPL, see 661 | . 662 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Atomic BlockChain Data Exchange with Fairness 2 | 3 | FDE protocols allow a server and a client to exchange KZG-committed data securely and fairly. 4 | The server holds all the data, while the client only knows a KZG (polynomial commitment) to the data. For more details on the protocol, refer to our research paper. 5 | This protocol is useful for Ethereum in a post [EIP-4844](https://github.com/ethereum/EIPs/blob/master/EIPS/eip-4844.md) world. In particular, blocks will contain blob data (KZG commitments) that commit to rollup data. The block header only contains KZG commitments, while full nodes store the entire data. It is reasonable to assume that an efficient market will emerge for downloading rollup data from full nodes. 6 | This work creates protocols that allow full nodes to exchange the committed data for money in an atomic and fair manner. 7 | 8 | Title: Atomic BlockChain Data Exchange with Fairness 9 | 10 | Authors: Ertem Nusret Tas, Valeria Nikolaenko, István A. Seres, Márk Melczer, Yinuo Zhang, Mahimna Kelkar, Joseph Bonneau. 11 | 12 | Currently available at the following link: 13 | * IACR [eprint link](https://eprint.iacr.org/2024/418.pdf). 14 | 15 | ## Quickstart 16 | 17 | The protocols in the paper are implemented in the [Rust programming language](https://www.rust-lang.org/), relying heavily on cryptographic libraries from [arkworks](https://github.com/arkworks-rs). The source code is found in [src](https://github.com/PopcornPaws/fde/tree/main/src). Respective smart contracts were implemented in [Solidity](https://soliditylang.org/) and they are found in [contracts](https://github.com/PopcornPaws/fde/tree/main/contracts). 18 | 19 | ### Installing, building, and running tests 20 | 21 | First, you must install `rustup` by following the steps outlined [here](https://www.rust-lang.org/learn/get-started). 22 | 23 | ```sh 24 | curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh 25 | ``` 26 | 27 | Clone the repository and jump into the cloned directory 28 | ```sh 29 | git clone https://github.com/PopcornPaws/fde.git 30 | cd fde 31 | ``` 32 | - build: `cargo build --release` (the `release` flag is optional) 33 | - test: `cargo test --release` (the `release` flag is optional) 34 | - benchmark: `cargo bench` 35 | 36 | ### Contracts 37 | Requires [Foundry](https://book.getfoundry.sh/getting-started/installation). 38 | 39 | Install: `forge install` 40 | 41 | Build: `forge build` 42 | 43 | Differential tests: `forge test --match-test testRef --ffi` 44 | 45 | Other tests: `forge test --no-match-test testRef` 46 | 47 | 48 | ## Implemented BDE protocols 49 | 50 | Below is a short introduction to the implementation of the protocols in the paper. 51 | **IMPORTANT** This is an unaudited, proof-of-concept implementation used mainly for benchmarking and exploring practical feasibility and limitations. Do not use this code in a production environment. 52 | 53 | ### ElGamal encryption-based 54 | 55 | This [version](https://github.com/PopcornPaws/fde/tree/main/src/veck/kzg/elgamal) of the protocol uses exponential ElGamal encryption for generating the ciphertexts. Plaintext data is represented by scalar field elements of the BLS12-381 curve. Since exponential ElGamal relies on a brute-force approach to decrypt the ciphertexts, we needed to ensure that the encrypted scalar field elements are split up into multiple `u32` shards that are easier to decrypt than a single 256-bit scalar. Thus we needed an additional [encryption proof](https://github.com/PopcornPaws/fde/blob/main/src/veck/kzg/elgamal/encryption.rs) whose goal is to prove that the plaintext shards are indeed in the range of `0..u32::MAX` and we also needed to ensure that the plaintext shards can be used to reconstruct the original 256 bit scalar. For this, we used simple [`DLEQ` proofs](https://github.com/PopcornPaws/fde/blob/main/src/dleq.rs). For the [range proofs](https://github.com/PopcornPaws/fde/tree/main/src/range_proof), we used a slightly modified version of [this](https://github.com/roynalnaruto/range_proof) implementation, that is based on the work of [Boneh-Fisch-Gabizon-Williamson](https://hackmd.io/@dabo/B1U4kx8XI) with further details discussed in [this blogpost](https://decentralizedthoughts.github.io/2020-03-03-range-proofs-from-polynomial-commitments-reexplained/). 56 | 57 | ### Paillier encryption-based 58 | 59 | This [version](https://github.com/PopcornPaws/fde/blob/main/src/veck/kzg/paillier/mod.rs) of the protocol uses the Paillier encryption scheme to encrypt the plaintext data. It utilizes the [num-bigint](https://crates.io/crates/num-bigint) crate for proof generation due to working in an RSA group instead of an elliptic curve. Computations are, therefore, slightly less performant than working with [arkworks](https://github.com/arkworks-rs) libraries, but we gain a lot in the decryption phase where there is no need to split up the original plaintext, generate range proofs, and use a brute-force approach for decryption. 60 | 61 | ## On-chain components of our protocols 62 | Our protocols apply smart contracts to achieve atomicity and fairness. Have a look at our [implemented FDE smart contracts](https://github.com/PopcornPaws/fde/blob/main/contracts/FDE.sol). 63 | ## Benchmarks 64 | We provide benchmarks in [this folder](https://github.com/PopcornPaws/fde/tree/main/benches). 65 | ## Contributing 66 | We welcome any contributions. Feel free to [open new issues](https://github.com/PopcornPaws/fde/issues/new) or [resolve existing ones](https://github.com/PopcornPaws/fde/issues). 67 | 68 | ## Disclaimer 69 | *The code is being provided as is. No guarantee, representation or warranty is being made, express or implied, as to the safety or correctness of the code. The code has not been audited and as such there can be no assurance it will work as intended, and users may experience delays, failures, errors, omissions or loss of transmitted information. THE CODE CONTAINED HEREIN IS FURNISHED AS IS, WHERE IS, WITH ALL FAULTS AND WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING ANY WARRANTY OF MERCHANTABILITY, NON- INFRINGEMENT OR FITNESS FOR ANY PARTICULAR PURPOSE. Further, use of any of the smart contracts may be restricted or prohibited under applicable law, including securities laws, and it is therefore strongly advised for you to contact a reputable attorney in any jurisdiction where these smart contracts may be accessible for any questions or concerns with respect thereto. Further, no information provided in this repo should be construed as investment advice or legal advice for any particular facts or circumstances, and is not meant to replace competent counsel. The authors are not liable for any use of the foregoing, and users should proceed with caution and use at their own risk.* 70 | -------------------------------------------------------------------------------- /benches/Figures/proofSizes.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/PopcornPaws/fde/0ae60c7ca544e78ba03ca7a5eccb55532dfb9674/benches/Figures/proofSizes.pdf -------------------------------------------------------------------------------- /benches/Figures/proverVerifierTimes.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/PopcornPaws/fde/0ae60c7ca544e78ba03ca7a5eccb55532dfb9674/benches/Figures/proverVerifierTimes.pdf -------------------------------------------------------------------------------- /benches/elgamal-plot.txt: -------------------------------------------------------------------------------- 1 | KZG-ELGAMAL - all units are [ms] 2 | proof-gen 154.86,87.448,50.783,34.127,25.760,21.619,19.509,19.157,20.204,22.213,24.984,30.279,38.948 3 | proof-vfy 6.03,7.64,7.69,7.97,8.19,8.75,9.42,10.68,12.25,15.28,19.86,28.90,42.23 4 | 5 | range-proof-vfy 11.77,21.79,34.44,68.23,127.09,253.12,500.32,1004.9,1991.1,4020.1,8039.2,16084.0,32133.0 6 | split-scalar-encryption-vfy 1.92,3.64,5.66,10.92,40.83,80.35,160.01,319.60,639.45,1277.1,2550.7 7 | 8 | total-proof-vfy 27.796,31.336,43.210,77.583,136.80,264.56,511.48,1014.4,2119.5,4383.4,8630.0,17055.0,34149.0 9 | 10 | range proofs + encryptions are pre-computed in 89 seconds 11 | -------------------------------------------------------------------------------- /benches/elgamal.rs: -------------------------------------------------------------------------------- 1 | use ark_bls12_381::{Bls12_381 as BlsCurve, G1Affine}; 2 | use ark_ec::pairing::Pairing; 3 | use ark_ec::{AffineRepr, CurveGroup}; 4 | use ark_ff::PrimeField; 5 | use ark_std::{test_rng, UniformRand}; 6 | use criterion::{criterion_group, criterion_main, Criterion}; 7 | use fde::encrypt::EncryptionEngine; 8 | #[cfg(feature = "parallel")] 9 | use rayon::prelude::*; 10 | 11 | const N: usize = Scalar::MODULUS_BIT_SIZE as usize / fde::encrypt::elgamal::MAX_BITS + 1; 12 | 13 | type Scalar = ::ScalarField; 14 | type SplitScalar = fde::encrypt::elgamal::SplitScalar<{ N }, Scalar>; 15 | type Elgamal = fde::encrypt::elgamal::ExponentialElgamal<::G1>; 16 | 17 | // NOTE in case of 4096 scalars, we have 4096 * N split scalars 18 | fn bench_elgamal(c: &mut Criterion) { 19 | let mut group = c.benchmark_group("split-elgamal"); 20 | group.sample_size(10); 21 | 22 | let rng = &mut test_rng(); 23 | let encryption_sk = Scalar::rand(rng); 24 | let encryption_pk = (G1Affine::generator() * encryption_sk).into_affine(); 25 | 26 | let scalars: Vec = (0..4096 * N).map(|_| Scalar::rand(rng)).collect(); 27 | 28 | let mut ciphers = Vec::with_capacity(scalars.len()); 29 | let mut split_ciphers = Vec::with_capacity(scalars.len()); 30 | 31 | println!("GENERATING ENCRYPTIONS..."); 32 | let now = std::time::Instant::now(); 33 | scalars.iter().enumerate().for_each(|(i, scalar)| { 34 | if i % 256 == 0 { 35 | println!("{}/{}", i, 4096 * N); 36 | } 37 | let split_scalar = SplitScalar::from(*scalar); 38 | let (split_cipher, randomness) = split_scalar.encrypt::(&encryption_pk, rng); 39 | let long_cipher = ::encrypt_with_randomness( 40 | &scalar, 41 | &encryption_pk, 42 | &randomness, 43 | ); 44 | 45 | ciphers.push(long_cipher); 46 | split_ciphers.push(split_cipher); 47 | }); 48 | let elapsed = std::time::Instant::now().duration_since(now).as_secs(); 49 | println!("ELAPSED: {} [s]", elapsed); 50 | 51 | for i in 0..=12 { 52 | let subset_size = 1 << i; 53 | let verify_split_encryption_name = format!("verify-split-encryption-{}", subset_size); 54 | group.bench_function(verify_split_encryption_name, |b| { 55 | b.iter(|| { 56 | #[cfg(not(feature = "parallel"))] 57 | ciphers 58 | .iter() 59 | .take(subset_size * N) 60 | .zip(&split_ciphers) 61 | .for_each(|(cipher, split_cipher)| { 62 | assert!(cipher.check_encrypted_sum(split_cipher)); 63 | }); 64 | #[cfg(feature = "parallel")] 65 | ciphers 66 | .par_iter() 67 | .take(subset_size * N) 68 | .zip(&split_ciphers) 69 | .for_each(|(long_cipher, split_cipher)| { 70 | assert!(long_cipher.check_encrypted_sum(split_cipher)); 71 | }); 72 | }) 73 | }); 74 | } 75 | 76 | group.finish() 77 | } 78 | 79 | criterion_group!(benches, bench_elgamal); 80 | criterion_main!(benches); 81 | -------------------------------------------------------------------------------- /benches/kzg_elgamal.rs: -------------------------------------------------------------------------------- 1 | use ark_ec::pairing::Pairing; 2 | use ark_ec::{CurveGroup, Group}; 3 | use ark_ff::PrimeField; 4 | use ark_poly::univariate::DensePolynomial; 5 | use ark_poly::{EvaluationDomain, Evaluations, GeneralEvaluationDomain}; 6 | use ark_std::{test_rng, UniformRand}; 7 | use criterion::{criterion_group, criterion_main, Criterion}; 8 | use fde::commit::kzg::Powers; 9 | 10 | const DATA_LOG_SIZE: usize = 12; // 4096 = 2^12 11 | const N: usize = Scalar::MODULUS_BIT_SIZE as usize / fde::encrypt::elgamal::MAX_BITS + 1; 12 | 13 | type TestCurve = ark_bls12_381::Bls12_381; 14 | type TestHash = sha3::Keccak256; 15 | type Scalar = ::ScalarField; 16 | type UniPoly = DensePolynomial; 17 | type Proof = fde::veck::kzg::elgamal::Proof<{ N }, TestCurve, TestHash>; 18 | type EncryptionProof = fde::veck::kzg::elgamal::EncryptionProof<{ N }, TestCurve, TestHash>; 19 | 20 | fn bench_proof(c: &mut Criterion) { 21 | let mut group = c.benchmark_group("kzg-elgamal"); 22 | group.sample_size(10); 23 | 24 | let data_size = 1 << DATA_LOG_SIZE; 25 | assert_eq!(data_size, 4096); 26 | 27 | let rng = &mut test_rng(); 28 | let tau = Scalar::rand(rng); 29 | let powers = Powers::::unsafe_setup(tau, data_size + 1); 30 | 31 | let encryption_sk = Scalar::rand(rng); 32 | let encryption_pk = (::G1::generator() * encryption_sk).into_affine(); 33 | 34 | println!("Generating encryption proofs for 4096 * 8 split field elements..."); 35 | println!("This might take a few minutes and it's not included in the actual benchmarks."); 36 | let t_start = std::time::Instant::now(); 37 | let data: Vec = (0..data_size).map(|_| Scalar::rand(rng)).collect(); 38 | let encryption_proof = EncryptionProof::new(&data, &encryption_pk, &powers, rng); 39 | let elapsed = std::time::Instant::now().duration_since(t_start).as_secs(); 40 | println!("Generated encryption proofs, elapsed time: {} [s]", elapsed); 41 | 42 | let domain = GeneralEvaluationDomain::new(data.len()).expect("valid domain"); 43 | let index_map = fde::veck::index_map(domain); 44 | 45 | let evaluations = Evaluations::from_vec_and_domain(data, domain); 46 | let f_poly: UniPoly = evaluations.interpolate_by_ref(); 47 | let com_f_poly = powers.commit_g1(&f_poly); 48 | 49 | for i in 0..=12 { 50 | let subset_size = 1 << i; 51 | let proof_gen_name = format!("proof-gen-{}", subset_size); 52 | let proof_vfy_name = format!("proof-vfy-{}", subset_size); 53 | 54 | let subdomain = GeneralEvaluationDomain::new(subset_size).unwrap(); 55 | let subset_indices = fde::veck::subset_indices(&index_map, &subdomain); 56 | let subset_evaluations = fde::veck::subset_evals(&evaluations, &subset_indices, subdomain); 57 | 58 | let f_s_poly: UniPoly = subset_evaluations.interpolate_by_ref(); 59 | let com_f_s_poly = powers.commit_g1(&f_s_poly); 60 | 61 | let sub_encryption_proof = encryption_proof.subset(&subset_indices); 62 | 63 | group.bench_function(&proof_gen_name, |b| { 64 | b.iter(|| { 65 | Proof::new( 66 | &f_poly, 67 | &f_s_poly, 68 | &encryption_sk, 69 | sub_encryption_proof.clone(), 70 | &powers, 71 | rng, 72 | ) 73 | .unwrap(); 74 | }) 75 | }); 76 | 77 | group.bench_function(&proof_vfy_name, |b| { 78 | let proof = Proof::new( 79 | &f_poly, 80 | &f_s_poly, 81 | &encryption_sk, 82 | sub_encryption_proof.clone(), 83 | &powers, 84 | rng, 85 | ) 86 | .unwrap(); 87 | b.iter(|| { 88 | assert!(proof 89 | .verify(com_f_poly, com_f_s_poly, encryption_pk, &powers) 90 | .is_ok()) 91 | }) 92 | }); 93 | } 94 | 95 | group.finish(); 96 | } 97 | 98 | criterion_group!(benches, bench_proof); 99 | criterion_main!(benches); 100 | -------------------------------------------------------------------------------- /benches/kzg_paillier.rs: -------------------------------------------------------------------------------- 1 | use ark_bls12_381::Bls12_381 as BlsCurve; 2 | use ark_ec::pairing::Pairing; 3 | use ark_ff::{BigInteger, PrimeField}; 4 | use ark_poly::univariate::DensePolynomial; 5 | use ark_poly::{EvaluationDomain, Evaluations, GeneralEvaluationDomain}; 6 | use ark_std::{test_rng, UniformRand}; 7 | use criterion::{criterion_group, criterion_main, Criterion}; 8 | use fde::commit::kzg::Powers; 9 | use fde::veck::kzg::paillier::Server; 10 | use num_bigint::BigUint; 11 | 12 | type TestCurve = ark_bls12_381::Bls12_381; 13 | type TestHash = sha3::Keccak256; 14 | type Scalar = ::ScalarField; 15 | type UniPoly = DensePolynomial; 16 | type PaillierEncryptionProof = fde::veck::kzg::paillier::Proof; 17 | 18 | fn bench_proof(c: &mut Criterion) { 19 | let mut group = c.benchmark_group("kzg-paillier"); 20 | group.sample_size(10); 21 | 22 | // TODO until subset openings don't work, use full open 23 | // https://github.com/PopcornPaws/fde/issues/9 24 | //let data_size = 1 << 12; 25 | //let data: Vec = (0..data_size).map(|_| Scalar::rand(rng)).collect(); 26 | //let domain = GeneralEvaluationDomain::new(DATA_SIZE).unwrap(); 27 | let rng = &mut test_rng(); 28 | let tau = Scalar::rand(rng); 29 | let powers = Powers::::unsafe_setup_eip_4844(tau, 1 << 12); // TODO data_size 30 | let server = Server::new(rng); 31 | 32 | for i in 0..=12 { 33 | // TODO remove this once subset proofs work https://github.com/PopcornPaws/fde/issues/9 34 | let data_size = 1 << i; 35 | let subset_size = 1 << i; 36 | let proof_gen_name = format!("proof-gen-{}", subset_size); 37 | let proof_vfy_name = format!("proof-vfy-{}", subset_size); 38 | let decryption_name = format!("decryption-{}", subset_size); 39 | // random data to encrypt 40 | let data: Vec = (0..data_size).map(|_| Scalar::rand(rng)).collect(); 41 | let domain = GeneralEvaluationDomain::new(data_size).unwrap(); 42 | let domain_s = GeneralEvaluationDomain::new(subset_size).unwrap(); 43 | let evaluations = Evaluations::from_vec_and_domain(data, domain); 44 | let index_map = fde::veck::index_map(domain); 45 | let subset_indices = fde::veck::subset_indices(&index_map, &domain_s); 46 | let evaluations_s = fde::veck::subset_evals(&evaluations, &subset_indices, domain_s); 47 | 48 | let f_poly: UniPoly = evaluations.interpolate_by_ref(); 49 | let f_s_poly: UniPoly = evaluations_s.interpolate_by_ref(); 50 | 51 | let evaluations_s_d = f_s_poly.evaluate_over_domain_by_ref(domain); 52 | 53 | let com_f_poly = powers.commit_scalars_g1(&evaluations.evals); 54 | let com_f_s_poly = powers.commit_scalars_g1(&evaluations_s_d.evals); 55 | 56 | let data_biguint: Vec = evaluations_s 57 | .evals 58 | .iter() 59 | .map(|d| BigUint::from_bytes_le(&d.into_bigint().to_bytes_le())) 60 | .collect(); 61 | 62 | group.bench_function(&proof_gen_name, |b| { 63 | b.iter(|| { 64 | PaillierEncryptionProof::new( 65 | &data_biguint, 66 | &f_poly, 67 | &f_s_poly, 68 | &com_f_poly, 69 | &com_f_s_poly, 70 | &domain, 71 | &domain_s, 72 | &server.pubkey, 73 | &powers, 74 | rng, 75 | ); 76 | }) 77 | }); 78 | 79 | group.bench_function(&proof_vfy_name, |b| { 80 | let proof = PaillierEncryptionProof::new( 81 | &data_biguint, 82 | &f_poly, 83 | &f_s_poly, 84 | &com_f_poly, 85 | &com_f_s_poly, 86 | &domain, 87 | &domain_s, 88 | &server.pubkey, 89 | &powers, 90 | rng, 91 | ); 92 | b.iter(|| { 93 | assert!(proof 94 | .verify( 95 | &com_f_poly, 96 | &com_f_s_poly, 97 | &domain, 98 | &domain_s, 99 | &server.pubkey, 100 | &powers 101 | ) 102 | .is_ok()); 103 | }) 104 | }); 105 | 106 | group.bench_function(&decryption_name, |b| { 107 | let proof = PaillierEncryptionProof::new( 108 | &data_biguint, 109 | &f_poly, 110 | &f_s_poly, 111 | &com_f_poly, 112 | &com_f_s_poly, 113 | &domain, 114 | &domain_s, 115 | &server.pubkey, 116 | &powers, 117 | rng, 118 | ); 119 | b.iter(|| { 120 | proof.decrypt(&server); 121 | }) 122 | }); 123 | } 124 | 125 | group.finish(); 126 | } 127 | 128 | criterion_group!(benches, bench_proof); 129 | criterion_main!(benches); 130 | -------------------------------------------------------------------------------- /benches/paillier-plot.txt: -------------------------------------------------------------------------------- 1 | KZG-PAILLIER - all units are [ms] 2 | gen 7.0327,11.586,14.667,14.188,23.555,43.434,83.285,163.02,321.44,641.81,1281.0,2549.2,5098.9 3 | vfy 6.6277,11.374,20.728,39.452,76.829,151.92,303.81,597.88,1203.2,2411.3,4861.1,9780.2,19455.0 4 | dec 4.7182,7.0237,11.507,20.714,38.926,75.921,148.84,296.96,598.35,1181.0,2373.0,4756.1,9541.7 5 | -------------------------------------------------------------------------------- /benches/plots.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | 4 | x_axis = [1<::ScalarField; 15 | type RangeProof = fde::range_proof::RangeProof; 16 | 17 | fn bench_proof(c: &mut Criterion) { 18 | let mut group = c.benchmark_group("range-proof"); 19 | 20 | let rng = &mut test_rng(); 21 | let tau = Scalar::rand(rng); 22 | let powers = Powers::::unsafe_setup(tau, 4 * LOG_2_UPPER_BOUND); 23 | 24 | let z = Scalar::from(100u32); 25 | 26 | group.bench_function("proof-gen", |b| { 27 | b.iter(|| { 28 | let _proof = RangeProof::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap(); 29 | }) 30 | }); 31 | 32 | group.bench_function("proof-vfy", |b| { 33 | let proof = RangeProof::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap(); 34 | b.iter(|| assert!(proof.verify(LOG_2_UPPER_BOUND, &powers).is_ok())) 35 | }); 36 | 37 | group.finish(); 38 | } 39 | 40 | // NOTE in case of 4096 scalars, we need 4096 * N range proofs for each smaller split scalar 41 | fn bench_multiple_proofs(c: &mut Criterion) { 42 | let mut group = c.benchmark_group("range-proof"); 43 | group.sample_size(10); 44 | 45 | let rng = &mut test_rng(); 46 | let tau = Scalar::rand(rng); 47 | let powers = Powers::::unsafe_setup(tau, 4 * LOG_2_UPPER_BOUND); 48 | 49 | let scalars: Vec = (0..4096 * N) 50 | .map(|_| Scalar::from(rng.next_u32())) 51 | .collect(); 52 | println!("GENERATING RANGE PROOFS..."); 53 | let now = std::time::Instant::now(); 54 | let proofs = scalars 55 | .into_iter() 56 | .enumerate() 57 | .inspect(|(i, _)| { 58 | if i % 256 == 0 { 59 | println!("{}/{}", i, 4096 * N); 60 | } 61 | }) 62 | .map(|(_, z)| RangeProof::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap()) 63 | .collect::>(); 64 | 65 | let elapsed = std::time::Instant::now().duration_since(now).as_secs(); 66 | println!("ELAPSED: {} [s]", elapsed); 67 | 68 | for i in 0..=12 { 69 | let subset_size = 1 << i; 70 | let range_proof_vfy_name = format!("range-proof-vfy-{}", subset_size); 71 | group.bench_function(range_proof_vfy_name, |b| { 72 | b.iter(|| { 73 | #[cfg(not(feature = "parallel"))] 74 | unimplemented!(); 75 | #[cfg(feature = "parallel")] 76 | proofs.par_iter().take(subset_size * N).for_each(|proof| { 77 | assert!(proof.verify(LOG_2_UPPER_BOUND, &powers).is_ok()); 78 | }); 79 | }) 80 | }); 81 | } 82 | } 83 | 84 | criterion_group!(benches, bench_multiple_proofs, bench_proof); 85 | criterion_main!(benches); 86 | -------------------------------------------------------------------------------- /contracts/BN254.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: MIT 2 | pragma solidity ^0.8.13; 3 | 4 | import { Types } from "./Types.sol"; 5 | import { Constants } from "./Constants.sol"; 6 | 7 | contract BN254 { 8 | /// @return the generator of G1 9 | // solhint-disable-next-line func-name-mixedcase 10 | function P1() internal pure returns (Types.G1Point memory) { 11 | return Types.G1Point(1, 2); 12 | } 13 | 14 | function P1Neg() internal pure returns (Types.G1Point memory) { 15 | return Types.G1Point(1, 0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD45); 16 | } 17 | 18 | /// @return the generator of G2 19 | // solhint-disable-next-line func-name-mixedcase 20 | function P2() internal pure returns (Types.G2Point memory) { 21 | return Types.G2Point({ 22 | x0: 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2, 23 | x1: 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed, 24 | y0: 0x090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b, 25 | y1: 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa 26 | }); 27 | } 28 | 29 | /* 30 | * @return The negation of p, i.e. p.plus(p.negate()) should be zero. 31 | */ 32 | function negate( 33 | Types.G1Point memory _p 34 | ) internal pure returns (Types.G1Point memory) { 35 | // The prime q in the base field F_q for G1 36 | if (_p.x == 0 && _p.y == 0) { 37 | return Types.G1Point(0, 0); 38 | } else { 39 | uint256 q = Constants.PRIME_Q; 40 | return Types.G1Point(_p.x, q - (_p.y % q)); 41 | } 42 | } 43 | 44 | /* 45 | * @return The multiplication of a G1 point with a scalar value. 46 | */ 47 | function mul( 48 | Types.G1Point memory _p, 49 | uint256 v 50 | ) internal view returns (Types.G1Point memory) { 51 | uint256[3] memory input; 52 | input[0] = _p.x; 53 | input[1] = _p.y; 54 | input[2] = v; 55 | 56 | Types.G1Point memory result; 57 | bool success; 58 | 59 | // solium-disable-next-line security/no-inline-assembly 60 | assembly { 61 | success := staticcall(sub(gas(), 2000), 7, input, 0x60, result, 0x40) 62 | switch success case 0 { revert(0, 0) } 63 | } 64 | require (success, "BN254: mul failed"); 65 | 66 | return result; 67 | } 68 | 69 | /* 70 | * @return Returns the sum of two G1 points. 71 | */ 72 | function plus( 73 | Types.G1Point memory p1, 74 | Types.G1Point memory p2 75 | ) internal view returns (Types.G1Point memory) { 76 | 77 | Types.G1Point memory result; 78 | bool success; 79 | 80 | uint256[4] memory input; 81 | input[0] = p1.x; 82 | input[1] = p1.y; 83 | input[2] = p2.x; 84 | input[3] = p2.y; 85 | 86 | // solium-disable-next-line security/no-inline-assembly 87 | assembly { 88 | success := staticcall(sub(gas(), 2000), 6, input, 0x80, result, 0x40) 89 | switch success case 0 { revert(0, 0) } 90 | } 91 | 92 | require(success, "BN254: plus failed"); 93 | 94 | return result; 95 | } 96 | 97 | // Return true if the following pairing product equals 1: 98 | // e(-a1, a2) * e(b1, b2) * e(c1, c2) 99 | // It is the caller's responsibility to ensure that the points are valid. 100 | function pairingCheck( 101 | Types.G1Point memory a1, 102 | Types.G2Point memory a2, 103 | Types.G1Point memory b1, 104 | Types.G2Point memory b2, 105 | Types.G1Point memory c1, 106 | Types.G2Point memory c2 107 | ) internal view returns (bool) { 108 | uint256 out; 109 | bool success; 110 | assembly { 111 | let mPtr := mload(0x40) 112 | // a1 113 | mstore(mPtr, mload(a1)) 114 | mstore(add(mPtr, 0x20), mload(add(a1, 0x20))) 115 | // a2 116 | mstore(add(mPtr, 0x40), mload(a2)) 117 | mstore(add(mPtr, 0x60), mload(add(a2, 0x20))) 118 | mstore(add(mPtr, 0x80), mload(add(a2, 0x40))) 119 | mstore(add(mPtr, 0xa0), mload(add(a2, 0x60))) 120 | // b1 121 | mstore(add(mPtr, 0xc0), mload(b1)) 122 | mstore(add(mPtr, 0xe0), mload(add(b1, 0x20))) 123 | // b2 124 | mstore(add(mPtr, 0x100), mload(b2)) 125 | mstore(add(mPtr, 0x120), mload(add(b2, 0x20))) 126 | mstore(add(mPtr, 0x140), mload(add(b2, 0x40))) 127 | mstore(add(mPtr, 0x160), mload(add(b2, 0x60))) 128 | // c1 129 | mstore(add(mPtr, 0x180), mload(c1)) 130 | mstore(add(mPtr, 0x1a0), mload(add(c1, 0x20))) 131 | // c2 132 | mstore(add(mPtr, 0x1c0), mload(c2)) 133 | mstore(add(mPtr, 0x1e0), mload(add(c2, 0x20))) 134 | mstore(add(mPtr, 0x200), mload(add(c2, 0x40))) 135 | mstore(add(mPtr, 0x220), mload(add(c2, 0x60))) 136 | 137 | success := staticcall(gas(), 8, mPtr, 0x240, 0x00, 0x20) 138 | out := mload(0x00) 139 | } 140 | require(success, "BN254: pairing check failed!"); 141 | return out == 1; 142 | } 143 | } -------------------------------------------------------------------------------- /contracts/Constants.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: MIT 2 | pragma solidity ^0.8.13; 3 | 4 | library Constants { 5 | // The base field 6 | uint256 constant PRIME_Q = 7 | 21888242871839275222246405745257275088696311157297823662689037894645226208583; 8 | 9 | // The scalar field 10 | uint256 constant PRIME_R = 11 | 21888242871839275222246405745257275088548364400416034343698204186575808495617; 12 | 13 | // Compute this value with Fr::from(128).inverse().unwrap() 14 | uint256 constant DOMAIN_SIZE_INV = 0x300385D5FB6F3CE964DFA52B147E55AC6DE38077E8C5FDB0215A31A8C8200001; 15 | uint256 constant LOG2_DOMAIN_SIZE = 7; 16 | 17 | // The 1st root of unity (counting from 0) of the subgroup domain. 18 | uint256 constant OMEGA = 0x16E73DFDAD310991DF5CE19CE85943E01DCB5564B6F24C799D0E470CBA9D1811; 19 | 20 | // The nth root of unity (counting from 0) of the subgroup domain. 21 | uint256 constant OMEGA_N = 0x1332CB377D53B9C681AFA4DC09F66BC37E3F2F33DEB33D9B40BD245C971B2447; 22 | 23 | // These values should be replaced with new ones from a trusted setup. 24 | // During development, remember to update these values if you use 25 | // unsafe_setup() or change the table size! 26 | 27 | // srs_g1[table_size] x and y and srs_g2[1] x0, x1, y0, and y1 28 | // from the output of https://github.com/geometryresearch/export-ptau-points 29 | // Using the Hermez Network phase 1 SRS (the 54th contribution of Perpetual 30 | // Powers of Tau plus a random beacon) 31 | 32 | // For a table size of 2 ^ 10: 33 | uint256 constant SRS_G1_T_X = 0x17A40BF6B2A82570FED3BEDB71E3DDF36680B431FFB3641FEC94F5478D34DCCC; 34 | uint256 constant SRS_G1_T_Y = 0x050852202323C504AAB1AE596553781B3DC87CC6793D731D054C7D751E82AF0A; 35 | 36 | // For a table size of 2 ^ 11: 37 | //uint256 constant SRS_G1_T_X = 0x195B22E5A84C5D5A70E8FAEA64DB9BFE8EB57577CFEB3A7798F5470C60B99BED; 38 | //uint256 constant SRS_G1_T_Y = 0x15D250AF555DC3DBF386C1BBDD00D9AB2B6908120041BC75F496A6FBE051A494; 39 | 40 | // For a table size of 2 ** 12: 41 | //uint256 constant SRS_G1_T_X = 0x160220880FDFD72FA9C1D4B6477B5AC9BF0310BE9C5C491F3F52EFD8573A2A14; 42 | //uint256 constant SRS_G1_T_Y = 0x094E210CAF49A96E4433927B1D17309B7724958FACADE891C041CDC196E4BCB8; 43 | 44 | // For a table size of 2 ** 14: 45 | //uint256 constant SRS_G1_T_X = 0x1820CAC999202BEBA571F32647CA77E38AA8AA2C6286857D68CAAA0C8F6EA688; 46 | //uint256 constant SRS_G1_T_Y = 0x1F93BBD6833793937E7971F0D99FDC98521C1869870763F17F0730850C476F69; 47 | 48 | // For a table size of 2 ** 16: 49 | //uint256 constant SRS_G1_T_X = 0x0E4753DD9EC507F7B9A3DB6069A6686872963B01D260378F4619E3166CA1481A; 50 | //uint256 constant SRS_G1_T_Y = 0x08DEAB995B28148852575D6BDB33AE1B5719861E09EC2FA4B6D295A74110BFCF; 51 | 52 | // For a table size of 2 ^ 20: 53 | //uint256 constant SRS_G1_T_X = 0x28ECE6AC832172CE0174B269049E9BF74F739090D042E277AFADB9B047937885; 54 | //uint256 constant SRS_G1_T_Y = 0x2C408B09EA45E3DC700AD3830D57080CA519AF5EDCABFCEB47EB64E08BB75D79; 55 | 56 | uint256 constant SRS_G2_1_X_0 = 0x26186A2D65EE4D2F9C9A5B91F86597D35F192CD120CAF7E935D8443D1938E23D; 57 | uint256 constant SRS_G2_1_X_1 = 0x30441FD1B5D3370482C42152A8899027716989A6996C2535BC9F7FEE8AAEF79E; 58 | uint256 constant SRS_G2_1_Y_0 = 0x1970EA81DD6992ADFBC571EFFB03503ADBBB6A857F578403C6C40E22D65B3C02; 59 | uint256 constant SRS_G2_1_Y_1 = 0x054793348F12C0CF5622C340573CB277586319DE359AB9389778F689786B1E48; 60 | } -------------------------------------------------------------------------------- /contracts/FDE.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: MIT 2 | pragma solidity ^0.8.13; 3 | 4 | import { BN254 } from "./BN254.sol"; 5 | import { Types } from "./Types.sol"; 6 | import { Constants } from "./Constants.sol"; 7 | 8 | 9 | // We could also have an almost identical contract that supports the Paillier-encryption scheme 10 | contract FDE is BN254 { 11 | 12 | struct agreedPurchase { 13 | uint256 timeOut; // The protocol after this timestamp, simply aborts and returns funds. 14 | uint256 agreedPrice; 15 | Types.G1Point sellerPubKey; 16 | bool ongoingPurchase; 17 | bool fundsLocked; 18 | } 19 | 20 | // We assume that for a given seller-buyer pair, there is only a single purchase at any given time 21 | // Maps seller (server addresses) to buyer (client addresses) which in turn are mapped to tx details 22 | mapping(address => mapping(address => agreedPurchase)) public orderBook; // Privacy is out of scope for now 23 | mapping(address => uint256) balances; //stores the Eth balances of sellers 24 | 25 | // Events 26 | event BroadcastPubKey(address indexed _seller, address indexed _buyer, uint256 _pubKeyX, uint256 _timeOut, uint256 _agreedPrice); 27 | event BroadcastSecKey(address indexed _seller, address indexed _buyer, uint256 _secKey); 28 | 29 | constructor ( 30 | ) { 31 | } 32 | 33 | // Agreed price could be set by the contract akin to Uniswap whereby price would be dynamically changing 34 | // according to a constant product formula given the current number of sellers and buyers (assuming 35 | // that each tx in the orderBook has the same volume) 36 | function sellerSendsPubKey( 37 | uint256 _timeOut, 38 | uint256 _agreedPrice, 39 | uint256 _pubKeyX, 40 | uint256 _pubKeyY, 41 | address _buyer 42 | ) public { 43 | require(!orderBook[msg.sender][_buyer].ongoingPurchase, "There can only be one purchase per buyer-seller pair!"); 44 | 45 | orderBook[msg.sender][_buyer] = agreedPurchase({ 46 | timeOut: _timeOut, 47 | agreedPrice: _agreedPrice, 48 | sellerPubKey: Types.G1Point(_pubKeyX, _pubKeyY), 49 | ongoingPurchase: true, 50 | fundsLocked: false 51 | }); 52 | 53 | emit BroadcastPubKey(msg.sender, _buyer, _pubKeyX, _timeOut, _agreedPrice); 54 | } 55 | 56 | // If buyer agrees to the details of the purchase, then it locks the corresponding amount of money. 57 | function buyerLockPayment( 58 | address _seller 59 | ) public payable { 60 | agreedPurchase memory order = orderBook[_seller][msg.sender]; 61 | 62 | requireOngoingPurchase(order); 63 | 64 | require(!order.fundsLocked, "Funds have been already locked!"); 65 | require(msg.value == order.agreedPrice, "The transferred money does not match the agreed price!"); 66 | 67 | orderBook[_seller][msg.sender].fundsLocked = true; 68 | } 69 | 70 | function sellerSendsSecKey( 71 | uint256 _secKey, 72 | address _buyer 73 | ) public { 74 | agreedPurchase memory order = orderBook[msg.sender][_buyer]; 75 | 76 | requireOngoingPurchase(order); 77 | 78 | require(mul(P1(),_secKey).x == order.sellerPubKey.x, "Invalid secret key has been provided by the seller!"); 79 | 80 | // this case is problematic for the seller, because they already revealed the secret key 81 | // but it is important for the health of the protocol that we don't increase their balance 82 | // if the funds have not been locked 83 | require(order.fundsLocked, "Funds have not been locked yet!"); 84 | 85 | _terminateOrder(msg.sender, _buyer); 86 | 87 | balances[msg.sender] += order.agreedPrice; 88 | 89 | // There is no need to store the secret key in storage 90 | emit BroadcastSecKey(msg.sender, _buyer, _secKey); 91 | } 92 | 93 | // This function allocates funds to the server from previous accrued purchase incomes 94 | function withdrawPayment( 95 | 96 | ) public { 97 | uint256 balance = balances[msg.sender]; 98 | if (balance != 0) { 99 | // We reset the balance to zero before the transfer to prevent reentrancy attacks 100 | balances[msg.sender] = 0; 101 | 102 | // forward all gas to the recipient 103 | (bool success, ) = payable(msg.sender).call{value: balance}(""); 104 | 105 | // revert on error 106 | require(success, "Transfer failed."); 107 | } 108 | } 109 | 110 | // Buyer can withdraw its money if seller does not reveal the correct secret key. 111 | function withdrawPaymentAfterTimeout( 112 | address _seller 113 | ) public { 114 | agreedPurchase memory order = orderBook[_seller][msg.sender]; 115 | 116 | requireOngoingPurchase(order); 117 | require(block.timestamp >= order.timeOut, "The seller has still time to provide the encryption secret key!"); 118 | require(order.fundsLocked, "Funds have not been locked yet!"); 119 | 120 | _terminateOrder(_seller, msg.sender); 121 | 122 | // forward all gas to the recipient 123 | (bool success, ) = payable(msg.sender).call{value: order.agreedPrice}(""); 124 | 125 | // revert on error 126 | require(success, "Transfer failed."); 127 | } 128 | 129 | /// Key function for state management: 130 | /// - can only have a single ongoing purchase per buyer-seller pair 131 | /// - order must be ongoing for valid state transition (locking funds, revealing key, triggering refund) 132 | /// 133 | /// reverts if: 134 | /// - the order never existed 135 | /// - it has completed successfully 136 | /// - it has expired 137 | function requireOngoingPurchase( 138 | agreedPurchase memory _order 139 | ) internal pure { 140 | require(_order.ongoingPurchase, "No such order"); 141 | } 142 | 143 | /// completely resets the state of an order (after expiration or completion) 144 | function _terminateOrder( 145 | address _seller, 146 | address _buyer 147 | ) internal { 148 | orderBook[_seller][_buyer] = agreedPurchase({ 149 | timeOut: 0, 150 | agreedPrice: 0, 151 | sellerPubKey: Types.G1Point(0, 0), 152 | ongoingPurchase: false, 153 | fundsLocked: false 154 | }); 155 | } 156 | } 157 | -------------------------------------------------------------------------------- /contracts/FDEPaillier.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: MIT 2 | pragma solidity ^0.8.13; 3 | 4 | import "./LibUint1024.sol"; 5 | 6 | 7 | // We could also have an almost identical contract that supports the Paillier-encryption scheme 8 | contract FDEPaillier { 9 | using LibUint1024 for *; 10 | 11 | uint256 public agreedPrice; 12 | uint256 public timeOut; // The protocol after this timestamp, sipmly aborts and returns funds. 13 | address public buyer; 14 | address public seller; 15 | uint256[4] public sellerPubKey; 16 | bool public secretKeySent; 17 | 18 | 19 | // Events 20 | event BroadcastPubKey(address indexed _seller, address indexed _buyer, uint256[4] _pubKey); 21 | event BroadcastSecKey(address indexed _seller, address indexed _buyer, uint256[4] _secKey); 22 | 23 | 24 | constructor ( 25 | uint256 _agreedPrice, 26 | uint256 _timeOut, 27 | address _buyer, 28 | address _seller 29 | ) { 30 | agreedPrice = _agreedPrice; 31 | timeOut = _timeOut; 32 | buyer = _buyer; 33 | seller = _seller; 34 | } 35 | 36 | // This function could be incorporated into the constructor? 37 | function sellerSendsPubKey( 38 | uint256[4] memory _pubKey 39 | ) public { 40 | require(msg.sender == seller, "Only the seller can provide the encryption public key!"); 41 | 42 | sellerPubKey = _pubKey; 43 | 44 | emit BroadcastPubKey(seller, buyer, _pubKey); 45 | } 46 | 47 | function buyerLockPayment( 48 | 49 | ) public payable { 50 | require(!secretKeySent, "Secret keys have been already revealed!"); 51 | require(msg.sender == buyer, "Only the buyer can lock the payment for the data!"); 52 | require(msg.value == agreedPrice, "The transferred money does not match the agreed price!"); 53 | } 54 | 55 | function sellerSendsSecKey( 56 | uint256[4] memory p, 57 | uint256[4] memory q 58 | ) public { 59 | require(msg.sender == seller); 60 | require(p.mulMod(q,[~uint256(0),~uint256(0),~uint256(0),~uint256(0)]).eq(sellerPubKey), "Invalid secret key has been provided by the seller!"); 61 | secretKeySent = true; 62 | // There is no need to store the secret key in storage 63 | emit BroadcastSecKey(seller, buyer, p); 64 | } 65 | 66 | // This function allocates funds to the server if it already sent the encryption secret keys 67 | function withdrawPayment( 68 | 69 | ) public { 70 | require(secretKeySent, "The encryption secret key has not been provided by the seller!"); 71 | payable(seller).transfer(address(this).balance); 72 | // selfdestruct(buyer); maybe we should clean up the storage? 73 | 74 | } 75 | 76 | function withdrawPaymentAfterTimout( 77 | 78 | ) public { 79 | require(!secretKeySent, "The encryption secret key has already been sent by the seller!"); 80 | require(block.timestamp >= timeOut, "The seller has still time to provide the encryption secret key!"); 81 | payable(buyer).transfer(address(this).balance); 82 | // selfdestruct(buyer); maybe we should clean up the storage? 83 | } 84 | } -------------------------------------------------------------------------------- /contracts/LibUint1024.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: AGPL-3.0 2 | pragma solidity ^0.8; 3 | 4 | 5 | /// @dev A library for big (1024-bit) number arithmetic, including modular arithmetic 6 | /// operations. 7 | library LibUint1024 { 8 | using LibUint1024 for *; 9 | 10 | uint256 private constant MAX_UINT = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff; 11 | 12 | error Overflow(uint256[4] a, uint256[4] b); 13 | error Underflow(uint256[4] a, uint256[4] b); 14 | 15 | /// @dev Converts a uint256 to its 1024-bit representation. 16 | function toUint1024(uint256 x) 17 | internal 18 | pure 19 | returns (uint256[4] memory bn) 20 | { 21 | bn[3] = x; 22 | } 23 | 24 | /// @dev Computes a + b, reverting on overflow. 25 | function add(uint256[4] memory a, uint256[4] memory b) 26 | internal 27 | pure 28 | returns (uint256[4] memory c) 29 | { 30 | uint256 carry; 31 | (c, carry) = _add(a, b); 32 | if (carry != 0) { 33 | revert Overflow(a, b); 34 | } 35 | } 36 | 37 | /// @dev Computes a - b, reverting on underflow. 38 | function sub(uint256[4] memory a, uint256[4] memory b) 39 | internal 40 | pure 41 | returns (uint256[4] memory c) 42 | { 43 | uint256 carry; 44 | (c, carry) = _sub(a, b); 45 | if (carry != 0) { 46 | revert Underflow(a, b); 47 | } 48 | } 49 | 50 | /// @dev Computes a + b, returning the 1024-bit result and the carry bit. 51 | function _add(uint256[4] memory a, uint256[4] memory b) 52 | internal 53 | pure 54 | returns (uint256[4] memory c, uint256 carry) 55 | { 56 | assembly { 57 | // c[3] = a[3] + b[3] 58 | let aWord := mload(add(a, 0x60)) 59 | let bWord := mload(add(b, 0x60)) 60 | let sum := add(aWord, bWord) 61 | mstore(add(c, 0x60), sum) 62 | // carry = c[3] < a[3] 63 | carry := lt(sum, aWord) 64 | 65 | // c[2] = a[2] + b[2] + carry 66 | aWord := mload(add(a, 0x40)) 67 | bWord := mload(add(b, 0x40)) 68 | sum := add(aWord, bWord) 69 | let cWord := add(sum, carry) 70 | mstore(add(c, 0x40), cWord) 71 | // carry = (a[2] + b[2] < a[2]) || (c[2] < a[2] + b[2]) 72 | carry := or(lt(sum, aWord), lt(cWord, sum)) 73 | 74 | // c[1] = a[1] + b[1] + carry 75 | aWord := mload(add(a, 0x20)) 76 | bWord := mload(add(b, 0x20)) 77 | sum := add(aWord, bWord) 78 | cWord := add(sum, carry) 79 | mstore(add(c, 0x20), cWord) 80 | // carry = (a[1] + b[1] < a[1]) || (c[1] < a[1] + b[1]) 81 | carry := or(lt(sum, aWord), lt(cWord, sum)) 82 | 83 | // c[0] = a[0] + b[0] + carry 84 | aWord := mload(a) 85 | bWord := mload(b) 86 | sum := add(aWord, bWord) 87 | cWord := add(sum, carry) 88 | mstore(c, cWord) 89 | // carry = (a[0] + b[0] < a[0]) || (c[0] < a[0] + b[0]) 90 | carry := or(lt(sum, aWord), lt(cWord, sum)) 91 | } 92 | } 93 | 94 | /// @dev Computes a - b, returning the 1024-bit result and the carry bit. 95 | function _sub(uint256[4] memory a, uint256[4] memory b) 96 | internal 97 | pure 98 | returns (uint256[4] memory c, uint256 carry) 99 | { 100 | assembly { 101 | // c[3] = a[3] - b[3] 102 | let aWord := mload(add(a, 0x60)) 103 | let bWord := mload(add(b, 0x60)) 104 | let diff := sub(aWord, bWord) 105 | mstore(add(c, 0x60), diff) 106 | // carry = a[3] < b[3] 107 | carry := lt(aWord, bWord) 108 | 109 | // c[2] = a[2] - b[2] 110 | aWord := mload(add(a, 0x40)) 111 | bWord := mload(add(b, 0x40)) 112 | diff := sub(aWord, bWord) 113 | mstore(add(c, 0x40), sub(diff, carry)) 114 | // carry = (a[2] < b[2]) || (c[2] < carry) 115 | carry := or(lt(aWord, bWord), lt(diff, carry)) 116 | 117 | // c[1] = a[1] - b[1] 118 | aWord := mload(add(a, 0x20)) 119 | bWord := mload(add(b, 0x20)) 120 | diff := sub(aWord, bWord) 121 | mstore(add(c, 0x20), sub(diff, carry)) 122 | // carry = (a[1] < b[1]) || (c[1] < carry) 123 | carry := or(lt(aWord, bWord), lt(diff, carry)) 124 | 125 | // c[0] = a[0] - b[0] 126 | aWord := mload(a) 127 | bWord := mload(b) 128 | diff := sub(aWord, bWord) 129 | mstore(c, sub(diff, carry)) 130 | // carry = (a[0] < b[0]) || (c[0] < carry) 131 | carry := or(lt(aWord, bWord), lt(diff, carry)) 132 | } 133 | } 134 | 135 | /// @dev a == b 136 | function eq(uint256[4] memory a, uint256[4] memory b) 137 | internal 138 | pure 139 | returns (bool) 140 | { 141 | return 142 | a[0] == b[0] && 143 | a[1] == b[1] && 144 | a[2] == b[2] && 145 | a[3] == b[3]; 146 | } 147 | 148 | /// @dev a > b 149 | function gt(uint256[4] memory a, uint256[4] memory b) 150 | internal 151 | pure 152 | returns (bool) 153 | { 154 | return _gt(a, b, false); 155 | } 156 | 157 | /// @dev a ≥ b 158 | function gte(uint256[4] memory a, uint256[4] memory b) 159 | internal 160 | pure 161 | returns (bool) 162 | { 163 | return _gt(a, b, true); 164 | } 165 | 166 | function _gt( 167 | uint256[4] memory a, 168 | uint256[4] memory b, 169 | bool trueIfEqual 170 | ) 171 | private 172 | pure 173 | returns (bool) 174 | { 175 | if (a[0] < b[0]) { 176 | return false; 177 | } else if (a[0] > b[0]) { 178 | return true; 179 | } 180 | if (a[1] < b[1]) { 181 | return false; 182 | } else if (a[1] > b[1]) { 183 | return true; 184 | } 185 | if (a[2] < b[2]) { 186 | return false; 187 | } else if (a[2] > b[2]) { 188 | return true; 189 | } 190 | if (a[3] < b[3]) { 191 | return false; 192 | } 193 | return trueIfEqual || a[3] > b[3]; 194 | } 195 | 196 | /// @dev a < b 197 | function lt(uint256[4] memory a, uint256[4] memory b) 198 | internal 199 | pure 200 | returns (bool) 201 | { 202 | return _lt(a, b, false); 203 | } 204 | 205 | /// a ≤ b 206 | function lte(uint256[4] memory a, uint256[4] memory b) 207 | internal 208 | pure 209 | returns (bool) 210 | { 211 | return _lt(a, b, true); 212 | } 213 | 214 | function _lt( 215 | uint256[4] memory a, 216 | uint256[4] memory b, 217 | bool trueIfEqual 218 | ) 219 | private 220 | pure 221 | returns (bool) 222 | { 223 | if (a[0] > b[0]) { 224 | return false; 225 | } else if (a[0] < b[0]) { 226 | return true; 227 | } 228 | if (a[1] > b[1]) { 229 | return false; 230 | } else if (a[1] < b[1]) { 231 | return true; 232 | } 233 | if (a[2] > b[2]) { 234 | return false; 235 | } else if (a[2] < b[2]) { 236 | return true; 237 | } 238 | if (a[3] > b[3]) { 239 | return false; 240 | } 241 | return trueIfEqual || a[3] < b[3]; 242 | } 243 | 244 | /// @dev Computes (a * b) % modulus. Assumes a < modulus and b < modulus. 245 | /// Based on the "schoolbook" multiplication algorithm, using the EXPMOD 246 | /// precompile to reduce by the modulus. 247 | function mulMod(uint256[4] memory a, uint256[4] memory b, uint256[4] memory modulus) 248 | internal 249 | view 250 | returns (uint256[4] memory result) 251 | { 252 | assembly { 253 | // Computes x + y and increments the carry value if 254 | // x + y overflows. 255 | function addWithCarry(x, y, carry) -> z, updatedCarry { 256 | z := add(x, y) 257 | updatedCarry := add(carry, lt(z, x)) 258 | } 259 | 260 | // Multiplies two 256-bit mumbers to obtain the full 512-bit 261 | // result. h/t Remco Bloemen for this implementation: 262 | // https://medium.com/wicketh/mathemagic-full-multiply-27650fec525d 263 | function mul512(x, y) -> r1, r0 { 264 | let mm := mulmod(x, y, MAX_UINT) 265 | r0 := mul(x, y) 266 | r1 := sub(sub(mm, r0), lt(mm, r0)) 267 | } 268 | 269 | // The implementation roughly follows the schoolbook method: 270 | 271 | // ===a[0]== ===a[1]== ===a[2]== ===a[3]== 272 | // x ===b[0]== ===b[1]== ===b[2]== ===b[3]== 273 | // ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 274 | // ======a[3]b[3]====== 275 | // ======a[2]b[3]====== 276 | // ======a[1]b[3]====== 277 | // ======a[0]b[3]====== 278 | // ======a[3]b[2]====== 279 | // ======a[2]b[2]====== 280 | // ======a[1]b[2]====== 281 | // ======a[0]b[2]====== 282 | // ======a[3]b[1]====== 283 | // ======a[2]b[1]====== 284 | // ======a[1]b[1]====== 285 | // ======a[0]b[1]====== 286 | // ======a[3]b[0]====== 287 | // ======a[2]b[0]====== 288 | // ======a[1]b[0]====== 289 | // ======a[0]b[0]====== 290 | // ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 291 | // | | | | | | | | 292 | // | | | | | | | | 293 | // r0 | r1 | r2 | r3 | r4 | r5 | r6 | r7 | 294 | 295 | // Each a[j]b[k] is computed using mul512, so the result occupies two words. 296 | // Let a[j]b[k].h and a[j]b[k].l denote the high and low words, respectively. 297 | 298 | // Each ri will be computed as the sum of all the words in its column, plus the 299 | // carry ci from r{i+1}. 300 | 301 | // For example: 302 | // r7 := a[3]b[3].l 303 | // r6 := a[3]b[3].h + a[2]b[3].l + a[3]b[2].l 304 | // c5 := the carry value from the above sum 305 | // r5 := a[2]b[3].h + a[3]b[2].h + a[1]b[3].l + a[2]b[2].l + a[3]b[1].l + c5 306 | // c4 :+ the carry value from the above sum 307 | // ...and so on 308 | 309 | let p := mload(0x40) 310 | 311 | // Load all four words of a 312 | let a0 := mload(a) 313 | let a1 := mload(add(a, 0x20)) 314 | let a2 := mload(add(a, 0x40)) 315 | let a3 := mload(add(a, 0x60)) 316 | 317 | // This is where the words of the multiplication result (before reduction) will go. 318 | let r0 := 0 319 | let r1 := 0 320 | let r2 := 0 321 | let r3 := 0 322 | let r4 := 0 323 | let r5 := 0 324 | let r6 := 0 325 | 326 | // These will keep track of the carry values for each column. 327 | let c0 := 0 328 | let c1 := 0 329 | let c2 := 0 330 | let c3 := 0 331 | let c4 := 0 332 | let c5 := 0 333 | 334 | let h := 0 335 | let l := 0 336 | 337 | // b[3] 338 | let bi := mload(add(b, 0x60)) 339 | 340 | // r6 = a[3]b[3].h 341 | // r7 = a[3]b[3].l 342 | r6, l := mul512(a3, bi) 343 | // r7 doesn't get an explicit stack variable, we just mstore it immediately. 344 | mstore(add(p, 0x140), l) 345 | 346 | // r5 = a[2]b[3].h 347 | // r6 += a[2]b[3].l 348 | // c5 = carry from above addition 349 | r5, l := mul512(a2, bi) 350 | r6, c5 := addWithCarry(r6, l, 0) 351 | 352 | // r4 = a[1]b[3].h 353 | // r5 += a[1]b[3].l 354 | // c4 = carry from above addition 355 | r4, l := mul512(a1, bi) 356 | r5, c4 := addWithCarry(r5, l, 0) 357 | 358 | // r3 = a[0]b[3].h 359 | // r4 += a[0]b[3].l 360 | // c3 = carry from above addition 361 | r3, l := mul512(a0, bi) 362 | r4, c3 := addWithCarry(r4, l, 0) 363 | 364 | // b[2] 365 | bi := mload(add(b, 0x40)) 366 | 367 | // r6 += a[3]b[2].l 368 | // c5 += carry from above addition 369 | // r5 += a[3]b[2].h 370 | // c4 += carry from above addition 371 | h, l := mul512(a3, bi) 372 | r6, c5 := addWithCarry(r6, l, c5) 373 | r5, c4 := addWithCarry(r5, h, c4) 374 | 375 | // r5 += a[2]b[2].l 376 | // c4 += carry from above addition 377 | // r4 += a[2]b[2].h 378 | // c3 += carry from above addition 379 | h, l := mul512(a2, bi) 380 | r5, c4 := addWithCarry(r5, l, c4) 381 | r4, c3 := addWithCarry(r4, h, c3) 382 | 383 | // r4 += a[1]b[2].l 384 | // c3 += carry from above addition 385 | // r3 += a[1]b[2].h 386 | // c2 += carry from above addition 387 | h, l := mul512(a1, bi) 388 | r4, c3 := addWithCarry(r4, l, c3) 389 | r3, c2 := addWithCarry(r3, h, c2) 390 | 391 | // r3 += a[0]b[2].l 392 | // c2 += carry from above addition 393 | // r2 += a[0]b[2].h 394 | // c1 += carry from above addition 395 | h, l := mul512(a0, bi) 396 | r3, c2 := addWithCarry(r3, l, c2) 397 | r2, c1 := addWithCarry(r2, h, c1) 398 | 399 | // b[1] 400 | bi := mload(add(b, 0x20)) 401 | 402 | // r5 += a[3]b[1].l 403 | // c4 += carry from above addition 404 | // r4 += a[3]b[1].h 405 | // c3 += carry from above addition 406 | h, l := mul512(a3, bi) 407 | r5, c4 := addWithCarry(r5, l, c4) 408 | r4, c3 := addWithCarry(r4, h, c3) 409 | 410 | // r4 += a[2]b[1].l 411 | // c3 += carry from above addition 412 | // r3 += a[2]b[1].h 413 | // c2 += carry from above addition 414 | h, l := mul512(a2, bi) 415 | r4, c3 := addWithCarry(r4, l, c3) 416 | r3, c2 := addWithCarry(r3, h, c2) 417 | 418 | // r3 += a[1]b[1].l 419 | // c2 += carry from above addition 420 | // r2 += a[1]b[1].h 421 | // c1 += carry from above addition 422 | h, l := mul512(a1, bi) 423 | r3, c2 := addWithCarry(r3, l, c2) 424 | r2, c1 := addWithCarry(r2, h, c1) 425 | 426 | // r2 += a[0]b[1].l 427 | // c1 += carry from above addition 428 | // r1 += a[0]b[1].h 429 | // c0 += carry from above addition 430 | h, l := mul512(a0, bi) 431 | r2, c1 := addWithCarry(r2, l, c1) 432 | r1, c0 := addWithCarry(r1, h, c0) 433 | 434 | // b[0] 435 | bi := mload(b) 436 | 437 | // r4 += a[3]b[0].l 438 | // c3 += carry from above addition 439 | // r3 += a[3]b[0].h 440 | // c2 += carry from above addition 441 | h, l := mul512(a3, bi) 442 | r4, c3 := addWithCarry(r4, l, c3) 443 | r3, c2 := addWithCarry(r3, h, c2) 444 | 445 | // r3 += a[2]b[0].l 446 | // c2 += carry from above addition 447 | // r2 += a[2]b[0].h 448 | // c1 += carry from above addition 449 | h, l := mul512(a2, bi) 450 | r3, c2 := addWithCarry(r3, l, c2) 451 | r2, c1 := addWithCarry(r2, h, c1) 452 | 453 | // r2 += a[1]b[0].l 454 | // c1 += carry from above addition 455 | // r1 += a[1]b[0].h 456 | // c0 += carry from above addition 457 | h, l := mul512(a1, bi) 458 | r2, c1 := addWithCarry(r2, l, c1) 459 | r1, c0 := addWithCarry(r1, h, c0) 460 | 461 | // r1 += a[0]b[0].l 462 | // c0 += carry from above addition 463 | // r0 = a[0]b[0].h 464 | r0, l := mul512(a0, bi) 465 | r1, c0 := addWithCarry(r1, l, c0) 466 | 467 | // r5 += c5 468 | // c4 += carry from above addition 469 | r5 := add(r5, c5) 470 | c4 := add(c4, lt(r5, c5)) 471 | 472 | // r4 += c4 473 | // c3 += carry from above addition 474 | r4 := add(r4, c4) 475 | c3 := add(c3, lt(r4, c4)) 476 | 477 | // r3 += c3 478 | // c2 += carry from above addition 479 | r3 := add(r3, c3) 480 | c2 := add(c2, lt(r3, c3)) 481 | 482 | // r2 += c2 483 | // c1 += carry from above addition 484 | r2 := add(r2, c2) 485 | c1 := add(c1, lt(r2, c2)) 486 | 487 | // r1 += c1 488 | // c0 += carry from above addition 489 | r1 := add(r1, c1) 490 | c0 := add(c0, lt(r1, c1)) 491 | 492 | // r0 += c0 (cannot overflow) 493 | mstore(add(p, 0x60), add(r0, c0)) 494 | 495 | // Use EXPMOD precompile to compute 496 | // (r ** 1) % modulus = r % modulus 497 | 498 | // Store parameters for the EXPMOD precompile 499 | mstore(p, 0x100) // Length of base (8 * 32 = 256 bytes) 500 | mstore(add(p, 0x20), 0x20) // Length of exponent 501 | mstore(add(p, 0x40), 0x80) // Length of modulus (4 * 32 = 128 bytes) 502 | 503 | // Store the base 504 | mstore(add(p, 0x80), r1) 505 | mstore(add(p, 0xa0), r2) 506 | mstore(add(p, 0xc0), r3) 507 | mstore(add(p, 0xe0), r4) 508 | mstore(add(p, 0x100), r5) 509 | mstore(add(p, 0x120), r6) 510 | 511 | // Store the exponent 512 | mstore(add(p, 0x160), 1) 513 | 514 | // Use Identity (0x04) precompile to memcpy the modulus 515 | if iszero(staticcall(gas(), 0x04, modulus, 0x80, add(p, 0x180), 0x80)) { 516 | revert(0, 0) 517 | } 518 | // Call 0x05 (EXPMOD) precompile 519 | if iszero(staticcall(gas(), 0x05, p, 0x200, result, 0x80)) { 520 | revert(0, 0) 521 | } 522 | 523 | // Update free memory pointer 524 | mstore(0x40, add(p, 0x200)) 525 | } 526 | } 527 | 528 | /// @dev Computes (a + b) % modulus. Assumes a < modulus and b < modulus. 529 | function addMod(uint256[4] memory a, uint256[4] memory b, uint256[4] memory modulus) 530 | internal 531 | pure 532 | returns (uint256[4] memory result) 533 | { 534 | uint256 carry; 535 | (result, carry) = _add(a, b); 536 | if (carry == 1 || result.gte(modulus)) { 537 | (result, ) = _sub(result, modulus); 538 | } 539 | } 540 | 541 | /// @dev Computes (a - b) % modulus. Assumes a < modulus and b < modulus. 542 | function subMod(uint256[4] memory a, uint256[4] memory b, uint256[4] memory modulus) 543 | internal 544 | pure 545 | returns (uint256[4] memory result) 546 | { 547 | if (a.gte(b)) { 548 | return a.sub(b); 549 | } else { 550 | return modulus.sub(b.sub(a)); 551 | } 552 | } 553 | 554 | /// @dev Computes (base ** exponent) % modulus 555 | function expMod(uint256[4] memory base, uint256 exponent, uint256[4] memory modulus) 556 | internal 557 | view 558 | returns (uint256[4] memory result) 559 | { 560 | assembly { 561 | // Get free memory pointer 562 | let p := mload(0x40) 563 | 564 | // Store parameters for the EXPMOD precompile 565 | mstore(p, 0x80) // Length of base (4 * 32 = 128 bytes) 566 | mstore(add(p, 0x20), 0x20) // Length of exponent (32 bytes) 567 | mstore(add(p, 0x40), 0x80) // Length of modulus (4 * 32 = 128 bytes) 568 | 569 | // Use Identity (0x04) precompile to memcpy the base 570 | if iszero(staticcall(gas(), 0x04, base, 0x80, add(p, 0x60), 0x80)) { 571 | revert(0, 0) 572 | } 573 | // Store the exponent 574 | mstore(add(p, 0xe0), exponent) 575 | // Use Identity (0x04) precompile to memcpy the modulus 576 | if iszero(staticcall(gas(), 0x04, modulus, 0x80, add(p, 0x100), 0x80)) { 577 | revert(0, 0) 578 | } 579 | // Call 0x05 (EXPMOD) precompile 580 | if iszero(staticcall(gas(), 0x05, p, 0x180, result, 0x80)) { 581 | revert(0, 0) 582 | } 583 | 584 | // Update free memory pointer 585 | mstore(0x40, add(p, 0x180)) 586 | } 587 | } 588 | 589 | /// @dev Computes (base ** exponent) % modulus 590 | function expMod( 591 | uint256[4] memory base, 592 | uint256[4] memory exponent, 593 | uint256[4] memory modulus 594 | ) 595 | internal 596 | view 597 | returns (uint256[4] memory result) 598 | { 599 | assembly { 600 | // Get free memory pointer 601 | let p := mload(0x40) 602 | 603 | // Store parameters for the EXPMOD precompile 604 | mstore(p, 0x80) // Length of base (4 * 32 = 128 bytes) 605 | mstore(add(p, 0x20), 0x80) // Length of exponent (4 * 32 = 128 bytes) 606 | mstore(add(p, 0x40), 0x80) // Length of modulus (4 * 32 = 128 bytes) 607 | 608 | // Use Identity (0x04) precompile to memcpy the base 609 | if iszero(staticcall(gas(), 0x04, base, 0x80, add(p, 0x60), 0x80)) { 610 | revert(0, 0) 611 | } 612 | // Use Identity (0x04) precompile to memcpy the exponent 613 | if iszero(staticcall(gas(), 0x04, exponent, 0x80, add(p, 0xe0), 0x80)) { 614 | revert(0, 0) 615 | } 616 | // Use Identity (0x04) precompile to memcpy the modulus 617 | if iszero(staticcall(gas(), 0x04, modulus, 0x80, add(p, 0x160), 0x80)) { 618 | revert(0, 0) 619 | } 620 | // Call 0x05 (EXPMOD) precompile 621 | if iszero(staticcall(gas(), 0x05, p, 0x1e0, result, 0x80)) { 622 | revert(0, 0) 623 | } 624 | 625 | // Update free memory pointer 626 | mstore(0x40, add(p, 0x1e0)) 627 | } 628 | } 629 | 630 | /// @dev Converts an element `x` of the RSA group Z_N to its "coset 631 | /// representative", defined to be min(x mod N, -x mod N). This ensures 632 | /// that the low-order assumption is not trivially false, see Section 6: 633 | /// http://crypto.stanford.edu/~dabo/papers/VDFsurvey.pdf 634 | function normalize( 635 | uint256[4] memory x, 636 | uint256[4] memory modulus 637 | ) 638 | internal 639 | pure 640 | returns (uint256[4] memory normalized) 641 | { 642 | uint256[4] memory negX = modulus.sub(x); 643 | if (negX.lt(x)) { 644 | return negX; 645 | } 646 | return x; 647 | } 648 | } -------------------------------------------------------------------------------- /contracts/Types.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: MIT 2 | pragma solidity ^0.8.13; 3 | 4 | library Types { 5 | struct G1Point { 6 | uint256 x; 7 | uint256 y; 8 | } 9 | // G2 group element where x \in Fq2 = x0 * z + x1 10 | struct G2Point { 11 | uint256 x0; 12 | uint256 x1; 13 | uint256 y0; 14 | uint256 y1; 15 | } 16 | 17 | struct ChallengeTranscript { 18 | /* 0x00 */ uint256 v; 19 | /* 0x20 */ uint256 hi_2; 20 | /* 0x40 */ uint256 alpha; 21 | /* 0x60 */ uint256 x1; 22 | /* 0x80 */ uint256 x2; 23 | /* 0xa0 */ uint256 x3; 24 | /* 0xc0 */ uint256 x4; 25 | /* 0xe0 */ uint256 s; 26 | } 27 | 28 | struct VerifierTranscript { 29 | /* 0x00 */ uint256 d; 30 | /* 0x20 */ uint256 omega_alpha; 31 | /* 0x40 */ uint256 omega_n_alpha; 32 | /* 0x60 */ uint256 dMinusOneInv; 33 | /* 0x80 */ uint256 xi_minus_v_inv; 34 | /* 0xa0 */ uint256 xi_minus_alpha_inv; 35 | /* 0xc0 */ uint256 xi_minus_omega_alpha_inv; 36 | /* 0xe0 */ uint256 xi_minus_omega_n_alpha_inv; 37 | /* 0x100 */ uint256 alpha_minus_omega_alpha_inv; 38 | /* 0x120 */ uint256 alpha_minus_omega_n_alpha_inv; 39 | /* 0x140 */ uint256 omega_alpha_minus_omega_n_alpha_inv; 40 | /* 0x160 */ uint256 l0Eval; 41 | /* 0x180 */ uint256 zhEval; 42 | /* 0x1a0 */ uint256 x1_pow_2; 43 | /* 0x1c0 */ uint256 x1_pow_3; 44 | /* 0x1e0 */ uint256 x1_pow_4; 45 | /* 0x200 */ uint256 x2_pow_2; 46 | /* 0x220 */ uint256 x2_pow_3; 47 | /* 0x240 */ uint256 x4_pow_2; 48 | /* 0x260 */ uint256 x4_pow_3; 49 | /* 0x280 */ uint256 x4_pow_4; 50 | /* 0x2a0 */ Types.G1Point q2; 51 | /* 0x2c0 */ Types.G1Point q4; 52 | /* 0x2e0 */ uint256 q4_at_alpha; 53 | /* 0x300 */ uint256 q4_at_omega_alpha; 54 | /* 0x320 */ uint256 q4_at_omega_n_alpha; 55 | /* 0x340 */ uint256 q2_eval; 56 | /* 0x360 */ uint256 f1; 57 | /* 0x380 */ uint256 f2; 58 | /* 0x3a0 */ uint256 f3; 59 | /* 0x3c0 */ uint256 f4; 60 | /* 0x3e0 */ uint256 xi_minus_omega_alpha; 61 | /* 0x400 */ uint256 xi_minus_alpha; 62 | /* 0x420 */ uint256 xi_minus_omega_n_alpha; 63 | /* 0x440 */ uint256 omega_alpha_minus_alpha_inv; 64 | /* 0x460 */ uint256 z3_xi; 65 | /* 0x480 */ uint256 f_eval; 66 | /* 0x4a0 */ Types.G1Point final_poly; 67 | /* 0x4c0 */ uint256 final_poly_eval; 68 | } 69 | 70 | struct Commitments { 71 | /* 0x00 */ Types.G1Point w0; 72 | /* 0x40 */ Types.G1Point w1; 73 | /* 0x80 */ Types.G1Point w2; 74 | /* 0xc0 */ Types.G1Point key; 75 | /* 0x100 */ Types.G1Point mimc_cts; 76 | /* 0x140 */ Types.G1Point quotient; 77 | /* 0x180 */ Types.G1Point u_prime; 78 | /* 0x1c0 */ Types.G1Point zi; 79 | /* 0x200 */ Types.G1Point ci; 80 | /* 0x240 */ Types.G1Point p1; 81 | /* 0x280 */ Types.G1Point p2; 82 | /* 0x2c0 */ Types.G1Point q_mimc; 83 | /* 0x300 */ Types.G1Point h; 84 | /* 0x340 */ Types.G2Point w; 85 | } 86 | 87 | struct Openings { 88 | /* 0x00 */ uint256 q_mimc; 89 | /* 0x20 */ uint256 mimc_cts; 90 | /* 0x40 */ uint256 quotient; 91 | /* 0x60 */ uint256 u_prime; 92 | /* 0x80 */ uint256 p1; 93 | /* 0xa0 */ uint256 p2; 94 | /* 0xc0 */ uint256 w0_0; 95 | /* 0xe0 */ uint256 w0_1; 96 | /* 0x100 */ uint256 w0_2; 97 | /* 0x120 */ uint256 w1_0; 98 | /* 0x140 */ uint256 w1_1; 99 | /* 0x160 */ uint256 w1_2; 100 | /* 0x180 */ uint256 w2_0; 101 | /* 0x1a0 */ uint256 w2_1; 102 | /* 0x1c0 */ uint256 w2_2; 103 | /* 0x1e0 */ uint256 key_0; 104 | /* 0x200 */ uint256 key_1; 105 | } 106 | 107 | struct MultiopenProof { 108 | /* 0x00 */ uint256 q1_opening; 109 | /* 0x20 */ uint256 q2_opening; 110 | /* 0x40 */ uint256 q3_opening; 111 | /* 0x60 */ uint256 q4_opening; 112 | /* 0x80 */ Types.G1Point f_cm; 113 | /* 0xa0 */ Types.G1Point final_poly_proof; 114 | } 115 | 116 | struct Proof { 117 | /* 0x00 */ MultiopenProof multiopenProof; 118 | /* 0x20 */ Openings openings; 119 | /* 0x40 */ Commitments commitments; 120 | } 121 | } -------------------------------------------------------------------------------- /src/adaptor_sig.rs: -------------------------------------------------------------------------------- 1 | use ark_crypto_primitives::signature::schnorr::{Schnorr, SecretKey, Signature}; 2 | use ark_crypto_primitives::signature::SignatureScheme; 3 | use ark_crypto_primitives::Error; 4 | use ark_ec::{AffineRepr, CurveGroup}; 5 | use ark_ff::Field; 6 | use ark_serialize::CanonicalSerialize; 7 | use ark_std::rand::Rng; 8 | use ark_std::UniformRand; 9 | use digest::Digest; 10 | 11 | pub trait AdaptorSignatureScheme: SignatureScheme { 12 | type PreSignature; 13 | 14 | fn pre_sign( 15 | adaptor_pk: &Self::PublicKey, 16 | signer_sk: &Self::SecretKey, 17 | message: &[u8], 18 | rng: &mut R, 19 | ) -> Result; 20 | 21 | fn verify( 22 | signature: &Self::PreSignature, 23 | adaptor_pk: &Self::PublicKey, 24 | signer_pk: &Self::PublicKey, 25 | message: &[u8], 26 | ) -> Result<(), Error>; 27 | 28 | fn adapt( 29 | signature: &Self::PreSignature, 30 | adaptor_sk: &Self::SecretKey, 31 | ) -> Result; 32 | 33 | fn extract( 34 | pre_signature: &Self::PreSignature, 35 | signature: &Self::Signature, 36 | adaptor_pk: &Self::PublicKey, 37 | ) -> Result; 38 | } 39 | 40 | impl AdaptorSignatureScheme for Schnorr { 41 | type PreSignature = Signature; 42 | fn pre_sign( 43 | adaptor_pk: &Self::PublicKey, 44 | signer_sk: &Self::SecretKey, 45 | message: &[u8], 46 | rng: &mut R, 47 | ) -> Result { 48 | let signer_pk = (::generator() * signer_sk.0).into_affine(); 49 | // random nonce (r) sampled uniformly 50 | let random_nonce = C::ScalarField::rand(rng); 51 | // commitment is shifted by the adaptor's pubkey 52 | // R_hat = r * G + Y 53 | let commitment = 54 | (::generator() * random_nonce + adaptor_pk).into_affine(); 55 | // compute challenge from public values (R_hat, X, m) 56 | let verifier_challenge = hash_challenge::(&commitment, &signer_pk, message)?; 57 | // s_hat = r - cx 58 | let prover_response = random_nonce - verifier_challenge * signer_sk.0; 59 | 60 | Ok(Signature { 61 | prover_response, 62 | verifier_challenge, 63 | }) 64 | } 65 | 66 | fn verify( 67 | signature: &Self::PreSignature, 68 | adaptor_pk: &Self::PublicKey, 69 | signer_pk: &Self::PublicKey, 70 | message: &[u8], 71 | ) -> Result<(), Error> { 72 | let &Signature { 73 | prover_response, 74 | verifier_challenge, 75 | } = signature; 76 | // s_hat * G + c * X + Y 77 | let commitment = ::generator() * prover_response 78 | + *signer_pk * verifier_challenge 79 | + adaptor_pk; 80 | // compute challenge 81 | let challenge = hash_challenge::(&commitment.into_affine(), signer_pk, message)?; 82 | if challenge != verifier_challenge { 83 | Err("verification failure".into()) 84 | } else { 85 | Ok(()) 86 | } 87 | } 88 | 89 | fn adapt( 90 | signature: &Self::PreSignature, 91 | adaptor_sk: &Self::SecretKey, 92 | ) -> Result { 93 | let &Signature { 94 | prover_response, 95 | verifier_challenge, 96 | } = signature; 97 | Ok(Signature { 98 | prover_response: prover_response + adaptor_sk.0, 99 | verifier_challenge, 100 | }) 101 | } 102 | 103 | fn extract( 104 | pre_signature: &Self::PreSignature, 105 | signature: &Self::Signature, 106 | adaptor_pk: &Self::PublicKey, 107 | ) -> Result { 108 | let &Signature { 109 | prover_response: pre_prover_response, 110 | .. 111 | } = pre_signature; 112 | let &Signature { 113 | prover_response, .. 114 | } = signature; 115 | let sk = prover_response - pre_prover_response; 116 | let pk = (::generator() * sk).into_affine(); 117 | if pk != *adaptor_pk { 118 | Err("invalid signatures".into()) 119 | } else { 120 | Ok(SecretKey(sk)) 121 | } 122 | } 123 | } 124 | 125 | fn hash_challenge( 126 | commitment: &C::Affine, 127 | signer_pk: &C::Affine, 128 | message: &[u8], 129 | ) -> Result { 130 | let mut hash_input = Vec::new(); 131 | commitment.serialize_compressed(&mut hash_input)?; 132 | signer_pk.serialize_compressed(&mut hash_input)?; 133 | message.serialize_compressed(&mut hash_input)?; 134 | 135 | C::ScalarField::from_random_bytes(&D::digest(&hash_input)) 136 | .ok_or::("invalid challenge".into()) 137 | } 138 | 139 | #[cfg(test)] 140 | mod test { 141 | use super::*; 142 | use ark_ec::Group; 143 | use ark_secp256k1::Projective as Secp256k1; 144 | use ark_std::test_rng; 145 | use sha3::Keccak256; 146 | 147 | type Scheme = Schnorr; 148 | 149 | fn keygen( 150 | rng: &mut R, 151 | ) -> ( 152 | ::PublicKey, 153 | ::SecretKey, 154 | ) { 155 | let mut parameters = Scheme::setup(rng).unwrap(); 156 | parameters.generator = Secp256k1::generator().into_affine(); 157 | Scheme::keygen(¶meters, rng).unwrap() 158 | } 159 | 160 | #[test] 161 | fn completeness() { 162 | // setup and keygen 163 | let rng = &mut test_rng(); 164 | let (signer_pk, signer_sk) = keygen(rng); 165 | let (adaptor_pk, adaptor_sk) = keygen(rng); 166 | 167 | // pre-signature generation 168 | let message = b"hello adaptor signature"; 169 | let pre_sig = Scheme::pre_sign(&adaptor_pk, &signer_sk, message, rng).unwrap(); 170 | // verify pre-signature 171 | assert!(::verify( 172 | &pre_sig, 173 | &adaptor_pk, 174 | &signer_pk, 175 | message 176 | ) 177 | .is_ok()); 178 | 179 | // adapt and verify signature 180 | let adapted_sig = Scheme::adapt(&pre_sig, &adaptor_sk).unwrap(); 181 | 182 | // s + y 183 | let commitment = Secp256k1::generator() * adapted_sig.prover_response 184 | + signer_pk * adapted_sig.verifier_challenge; 185 | 186 | let challenge = 187 | hash_challenge::(&commitment.into_affine(), &signer_pk, message) 188 | .unwrap(); 189 | 190 | assert_eq!(challenge, adapted_sig.verifier_challenge); 191 | 192 | // extract adaptor secret key 193 | let extracted_sk = Scheme::extract(&pre_sig, &adapted_sig, &adaptor_pk).unwrap(); 194 | assert_eq!(extracted_sk.0, adaptor_sk.0); 195 | } 196 | 197 | #[test] 198 | fn soundness() { 199 | // setup and keygen 200 | let rng = &mut test_rng(); 201 | let (signer_pk, signer_sk) = keygen(rng); 202 | let (adaptor_pk, _adaptor_sk) = keygen(rng); 203 | 204 | let message = b"hello adaptor signature"; 205 | 206 | // pre-signature generation (with invalid adaptor pubkey) 207 | let pre_sig = Scheme::pre_sign(&signer_pk, &signer_sk, message, rng).unwrap(); 208 | assert!(::verify( 209 | &pre_sig, 210 | &adaptor_pk, 211 | &signer_pk, 212 | message 213 | ) 214 | .is_err()); 215 | 216 | // pre-signature generation (with invalid message pubkey) 217 | let pre_sig = Scheme::pre_sign(&adaptor_pk, &signer_sk, b"invalid", rng).unwrap(); 218 | assert!(::verify( 219 | &pre_sig, 220 | &adaptor_pk, 221 | &signer_pk, 222 | message 223 | ) 224 | .is_err()); 225 | 226 | // valid pre-signature 227 | let pre_sig = Scheme::pre_sign(&adaptor_pk, &signer_sk, message, rng).unwrap(); 228 | assert!(::verify( 229 | &pre_sig, 230 | &adaptor_pk, 231 | &signer_pk, 232 | message 233 | ) 234 | .is_ok()); 235 | 236 | // adapt with invalid secret key 237 | let adapted_sig = Scheme::adapt(&pre_sig, &signer_sk).unwrap(); 238 | // signature will be invalid, thus it will be rejected when checked by a 3rd party 239 | // s + y 240 | let commitment = Secp256k1::generator() * adapted_sig.prover_response 241 | + signer_pk * adapted_sig.verifier_challenge; 242 | 243 | let challenge = 244 | hash_challenge::(&commitment.into_affine(), &signer_pk, message) 245 | .unwrap(); 246 | 247 | assert_ne!(challenge, adapted_sig.verifier_challenge); 248 | 249 | // extract invalid adaptor secret key 250 | assert!(Scheme::extract(&pre_sig, &adapted_sig, &adaptor_pk).is_err()); 251 | } 252 | } 253 | -------------------------------------------------------------------------------- /src/commit/kzg.rs: -------------------------------------------------------------------------------- 1 | // We need to commit to G2 as well, which arkworks' kzg10 implementation doesn't allow 2 | use ark_ec::pairing::Pairing; 3 | use ark_ec::{AffineRepr, CurveGroup, VariableBaseMSM as Msm}; 4 | use ark_ff::PrimeField; 5 | use ark_poly::univariate::DensePolynomial; 6 | use ark_poly::{EvaluationDomain, GeneralEvaluationDomain}; 7 | use ark_poly_commit::DenseUVPolynomial; 8 | use ark_std::marker::PhantomData; 9 | use ark_std::rand::Rng; 10 | use ark_std::{One, UniformRand, Zero}; 11 | 12 | pub struct Powers { 13 | pub g1: Vec, 14 | pub g2: Vec, 15 | } 16 | 17 | impl Powers { 18 | pub fn unsafe_setup(tau: C::ScalarField, range: usize) -> Self { 19 | let mut g1 = Vec::new(); 20 | let mut g2 = Vec::new(); 21 | let mut exponent = C::ScalarField::one(); 22 | for _ in 1..=range { 23 | g1.push((::generator() * exponent).into_affine()); 24 | g2.push((::generator() * exponent).into_affine()); 25 | exponent *= tau; 26 | } 27 | Self { g1, g2 } 28 | } 29 | 30 | pub fn unsafe_setup_eip_4844(tau: C::ScalarField, range: usize) -> Self { 31 | let mut g1 = Vec::new(); 32 | let mut g2 = Vec::new(); 33 | let domain = GeneralEvaluationDomain::new(range).unwrap(); 34 | let lagrange_evaluations = domain.evaluate_all_lagrange_coefficients(tau); 35 | lagrange_evaluations.into_iter().for_each(|exponent| { 36 | g1.push((::generator() * exponent).into_affine()); 37 | g2.push((::generator() * exponent).into_affine()); 38 | }); 39 | 40 | Self { g1, g2 } 41 | } 42 | 43 | pub fn commit_scalars_g1(&self, scalars: &[C::ScalarField]) -> C::G1 { 44 | Msm::msm_unchecked(&self.g1[0..scalars.len()], scalars) 45 | } 46 | 47 | pub fn commit_scalars_g2(&self, scalars: &[C::ScalarField]) -> C::G2 { 48 | Msm::msm_unchecked(&self.g2[0..scalars.len()], scalars) 49 | } 50 | 51 | pub fn commit_g1>( 52 | &self, 53 | poly: &P, 54 | ) -> C::G1 { 55 | self.commit_scalars_g1(poly.coeffs()) 56 | } 57 | 58 | pub fn commit_g2>( 59 | &self, 60 | poly: &P, 61 | ) -> C::G2 { 62 | self.commit_scalars_g2(poly.coeffs()) 63 | } 64 | 65 | pub fn g1_tau(&self) -> C::G1Affine { 66 | self.g1[1] 67 | } 68 | 69 | pub fn g2_tau(&self) -> C::G2Affine { 70 | self.g2[1] 71 | } 72 | 73 | pub fn g2_tau_squared(&self) -> C::G2Affine { 74 | self.g2[2] 75 | } 76 | } 77 | 78 | pub struct Kzg(PhantomData); 79 | 80 | impl Kzg { 81 | pub fn witness( 82 | poly: &DensePolynomial, 83 | point: C::ScalarField, 84 | ) -> DensePolynomial { 85 | let divisor = DensePolynomial::from_coefficients_slice(&[-point, C::ScalarField::one()]); 86 | poly / &divisor 87 | } 88 | 89 | pub fn aggregate_witness( 90 | polys: &[DensePolynomial], 91 | point: C::ScalarField, 92 | challenge: C::ScalarField, 93 | ) -> DensePolynomial { 94 | let aggregated = aggregate_polys(polys, challenge); 95 | Self::witness(&aggregated, point) 96 | } 97 | 98 | pub fn proof( 99 | poly: &DensePolynomial, 100 | point: C::ScalarField, 101 | value: C::ScalarField, 102 | powers: &Powers, 103 | ) -> C::G1Affine { 104 | let numerator = poly + &DensePolynomial::from_coefficients_slice(&[-value]); 105 | let quotient = Self::witness(&numerator, point); 106 | powers.commit_g1("ient).into() 107 | } 108 | 109 | pub fn verify_scalar( 110 | proof: C::G1Affine, 111 | commitment: C::G1Affine, 112 | point: C::ScalarField, 113 | value: C::ScalarField, 114 | powers: &Powers, 115 | ) -> bool { 116 | let point_g2 = C::G2Affine::generator() * point; 117 | let value_g1 = C::G1Affine::generator() * value; 118 | Self::verify(proof, commitment, point_g2, value_g1, powers) 119 | } 120 | 121 | pub fn verify( 122 | proof: C::G1Affine, 123 | commitment: C::G1Affine, 124 | point: C::G2, 125 | value: C::G1, 126 | powers: &Powers, 127 | ) -> bool { 128 | // com / g^y 129 | let com_over_g_value = commitment.into_group() - value; 130 | // g^{tau} / g^x 131 | let g_tau_over_g_point = powers.g2_tau().into_group() - point; 132 | 133 | Self::pairing_check(com_over_g_value, proof.into_group(), g_tau_over_g_point) 134 | } 135 | 136 | pub fn pairing_check(lhs_g1: C::G1, rhs_g1: C::G1, rhs_g2: C::G2) -> bool { 137 | let lhs = C::pairing(lhs_g1, C::G2Affine::generator()); 138 | let rhs = C::pairing(rhs_g1, rhs_g2); 139 | lhs == rhs 140 | } 141 | 142 | pub fn batch_verify( 143 | proofs: &[C::G1Affine], 144 | commitments: &[C::G1Affine], 145 | points: &[C::ScalarField], 146 | values: &[C::ScalarField], 147 | powers: &Powers, 148 | rng: &mut R, 149 | ) -> bool { 150 | // NOTE copied (and slightly modified) from 151 | // https://docs.rs/ark-poly-commit/latest/src/ark_poly_commit/kzg10/mod.rs.html#334-353 152 | // because we need a more flexible KZG implementation 153 | let mut total_c = ::zero(); 154 | let mut total_w = ::zero(); 155 | 156 | let mut randomizer = C::ScalarField::one(); 157 | // Instead of multiplying g and gamma_g in each turn, we simply accumulate 158 | // their coefficients and perform a final multiplication at the end. 159 | let mut g_multiplier = C::ScalarField::zero(); 160 | let gamma_g_multiplier = C::ScalarField::zero(); 161 | for (((c, &z), v), &w) in commitments.iter().zip(points).zip(values).zip(proofs) { 162 | let mut temp = w * z; 163 | temp += c; 164 | let c = temp; 165 | g_multiplier += &(randomizer * v); 166 | total_c += c * randomizer; 167 | total_w += w * randomizer; 168 | // We don't need to sample randomizers from the full field, 169 | // only from 128-bit strings. 170 | randomizer = u128::rand(rng).into(); 171 | } 172 | total_c -= C::G1Affine::generator() * g_multiplier; 173 | total_c -= powers.g1_tau() * gamma_g_multiplier; 174 | 175 | let affine_points = C::G1::normalize_batch(&[-total_w, total_c]); 176 | let (total_w, total_c) = (affine_points[0], affine_points[1]); 177 | 178 | C::multi_pairing( 179 | [total_w, total_c], 180 | [powers.g2_tau(), C::G2Affine::generator()], 181 | ) 182 | .0 183 | .is_one() 184 | } 185 | } 186 | 187 | pub fn aggregate_polys(values: &[DensePolynomial], by: S) -> DensePolynomial { 188 | let mut acc = S::one(); 189 | let mut result = DensePolynomial::zero(); 190 | 191 | for value in values { 192 | let tmp = value * &DensePolynomial { coeffs: vec![acc] }; 193 | result += &tmp; 194 | acc *= by; 195 | } 196 | 197 | result 198 | } 199 | 200 | #[cfg(test)] 201 | mod test { 202 | use super::*; 203 | use ark_bls12_381::Bls12_381 as BlsCurve; 204 | use ark_ec::CurveGroup; 205 | use ark_poly::univariate::DensePolynomial; 206 | use ark_poly::Polynomial; 207 | use ark_std::{test_rng, One}; 208 | 209 | type Scalar = ::ScalarField; 210 | type UniPoly = DensePolynomial; 211 | 212 | #[test] 213 | fn commitment() { 214 | let tau = Scalar::from(2); 215 | // 3 - 2x + x^2 216 | let poly = 217 | UniPoly::from_coefficients_slice(&[Scalar::from(3), -Scalar::from(2), Scalar::one()]); 218 | let poly_tau = poly.evaluate(&tau); 219 | assert_eq!(poly_tau, Scalar::from(3)); 220 | // kzg 221 | let powers = Powers::::unsafe_setup(tau, 10); 222 | let com_g1 = powers.commit_g1(&poly); 223 | let com_g2 = powers.commit_g2(&poly); 224 | 225 | assert_eq!(com_g1, (powers.g1[0] * poly_tau).into_affine()); 226 | assert_eq!(com_g2, (powers.g2[0] * poly_tau).into_affine()); 227 | } 228 | 229 | #[test] 230 | fn batch_verification() { 231 | let rng = &mut test_rng(); 232 | for _ in 0..10 { 233 | let mut degree = 0; 234 | while degree <= 1 { 235 | degree = usize::rand(rng) % 20; 236 | } 237 | 238 | let tau = Scalar::rand(rng); 239 | let powers = Powers::::unsafe_setup(tau, degree + 1); 240 | 241 | let mut comms = Vec::new(); 242 | let mut values = Vec::new(); 243 | let mut points = Vec::new(); 244 | let mut proofs = Vec::new(); 245 | for _ in 0..10 { 246 | let poly = UniPoly::rand(degree, rng); 247 | let comm = powers.commit_g1(&poly).into_affine(); 248 | let point = Scalar::rand(rng); 249 | let value = poly.evaluate(&point); 250 | let proof = Kzg::proof(&poly, point, value, &powers); 251 | assert!(Kzg::verify_scalar(proof, comm, point, value, &powers)); 252 | 253 | comms.push(comm); 254 | values.push(value); 255 | points.push(point); 256 | proofs.push(proof); 257 | } 258 | assert!(Kzg::batch_verify( 259 | &proofs, &comms, &points, &values, &powers, rng 260 | )); 261 | } 262 | } 263 | 264 | #[test] 265 | fn commitment_equality() { 266 | let rng = &mut test_rng(); 267 | let degree: usize = 16; 268 | let domain = GeneralEvaluationDomain::new(degree).unwrap(); 269 | let tau = Scalar::rand(rng); 270 | let powers = Powers::::unsafe_setup(tau, degree); 271 | let powers_eip = Powers::::unsafe_setup_eip_4844(tau, degree); 272 | 273 | let coeffs = (0..degree).map(|_| Scalar::rand(rng)).collect(); 274 | let poly = UniPoly { coeffs }; 275 | 276 | let evals = poly.evaluate_over_domain_by_ref(domain); 277 | let com_p = powers.commit_g1(&poly); 278 | let com_p_eip = powers_eip.commit_scalars_g1(&evals.evals); 279 | 280 | assert_eq!(com_p, com_p_eip); 281 | } 282 | } 283 | -------------------------------------------------------------------------------- /src/commit/mod.rs: -------------------------------------------------------------------------------- 1 | pub mod kzg; 2 | -------------------------------------------------------------------------------- /src/dleq.rs: -------------------------------------------------------------------------------- 1 | use crate::hash::Hasher; 2 | use ark_ec::CurveGroup; 3 | use ark_ff::PrimeField; 4 | use ark_std::marker::PhantomData; 5 | use ark_std::rand::Rng; 6 | use ark_std::UniformRand; 7 | use digest::Digest; 8 | 9 | pub struct Proof { 10 | pub challenge: C::ScalarField, 11 | pub claim: C::ScalarField, 12 | _digest: PhantomData, 13 | } 14 | 15 | impl Proof 16 | where 17 | C: CurveGroup, 18 | D: Digest, 19 | { 20 | pub fn new(secret: &C::ScalarField, g1: C::Affine, g2: C::Affine, rng: &mut R) -> Self { 21 | let rand = C::ScalarField::rand(rng); 22 | let k1 = g1 * rand; 23 | let k2 = g2 * rand; 24 | let h1 = g1 * secret; 25 | let h2 = g2 * secret; 26 | 27 | let mut hasher = Hasher::::new(); 28 | hasher.update(&k1); 29 | hasher.update(&k2); 30 | hasher.update(&h1); 31 | hasher.update(&h2); 32 | let hash_output = hasher.finalize(); 33 | 34 | let challenge = C::ScalarField::from_le_bytes_mod_order(&hash_output); 35 | let claim = rand - challenge * secret; 36 | 37 | Self { 38 | challenge, 39 | claim, 40 | _digest: PhantomData, 41 | } 42 | } 43 | 44 | pub fn verify(&self, g1: C::Affine, h1: C, g2: C::Affine, h2: C) -> bool { 45 | let k1 = g1 * self.claim + h1 * self.challenge; 46 | let k2 = g2 * self.claim + h2 * self.challenge; 47 | 48 | let mut hasher = Hasher::::new(); 49 | hasher.update(&k1); 50 | hasher.update(&k2); 51 | hasher.update(&h1); 52 | hasher.update(&h2); 53 | let hash_output = hasher.finalize(); 54 | 55 | let challenge = C::ScalarField::from_le_bytes_mod_order(&hash_output); 56 | 57 | challenge == self.challenge 58 | } 59 | } 60 | 61 | #[cfg(test)] 62 | mod test { 63 | use super::*; 64 | use crate::tests::{G1Affine, Scalar, TestCurve, TestHash}; 65 | use ark_ec::pairing::Pairing; 66 | use ark_ec::{AffineRepr, CurveGroup}; 67 | use ark_std::{test_rng, UniformRand}; 68 | 69 | type DleqProof = Proof<::G1, TestHash>; 70 | 71 | #[test] 72 | fn completeness() { 73 | let rng = &mut test_rng(); 74 | 75 | let g1 = G1Affine::generator(); 76 | let g2 = (G1Affine::generator() * Scalar::rand(rng)).into_affine(); 77 | 78 | let secret = Scalar::rand(rng); 79 | 80 | let h1 = g1 * secret; 81 | let h2 = g2 * secret; 82 | 83 | let proof = DleqProof::new(&secret, g1, g2, rng); 84 | 85 | assert!(proof.verify(g1, h1, g2, h2)); 86 | } 87 | 88 | #[test] 89 | fn soundness() { 90 | let rng = &mut test_rng(); 91 | 92 | let g1 = G1Affine::generator(); 93 | let g2 = (G1Affine::generator() * Scalar::rand(rng)).into_affine(); 94 | 95 | let secret = Scalar::rand(rng); 96 | 97 | let h1 = g1 * secret; 98 | let h2 = g2 * secret; 99 | 100 | // invalid secret 101 | let proof = DleqProof::new(&(secret * Scalar::from(2)), g1, g2, rng); 102 | assert!(!proof.verify(g1, h1, g2, h2)); 103 | 104 | // invalid point 105 | let proof = DleqProof::new(&secret, g1, g2, rng); 106 | assert!(!proof.verify(g1, h1, g1, h1)); 107 | } 108 | } 109 | -------------------------------------------------------------------------------- /src/encrypt/elgamal/mod.rs: -------------------------------------------------------------------------------- 1 | mod split_scalar; 2 | mod utils; 3 | 4 | pub use split_scalar::SplitScalar; 5 | use utils::shift_scalar; 6 | 7 | use super::EncryptionEngine; 8 | use ark_ec::{AffineRepr, CurveGroup}; 9 | use ark_std::marker::PhantomData; 10 | use ark_std::ops::{Add, Mul}; 11 | use ark_std::rand::Rng; 12 | use ark_std::{One, UniformRand, Zero}; 13 | 14 | pub const MAX_BITS: usize = 32; 15 | 16 | pub struct ExponentialElgamal(pub PhantomData); 17 | 18 | /// Exponential Elgamal encryption scheme ciphertext. 19 | /// 20 | /// It contains `c1 = g^y` and `c2 = g^m * h^y` where `g` is a group generator, `h = g^x` is the 21 | /// public encryption key computed from the secret `x` key, `y` is some random scalar and `m` is 22 | /// the message to be encrypted. 23 | #[derive(Clone, Copy, Debug, Eq, PartialEq)] 24 | pub struct Cipher([C::Affine; 2]); 25 | 26 | impl Default for Cipher { 27 | fn default() -> Self { 28 | Self::zero() 29 | } 30 | } 31 | 32 | impl Zero for Cipher { 33 | fn zero() -> Self { 34 | Self([C::Affine::zero(); 2]) 35 | } 36 | 37 | fn is_zero(&self) -> bool { 38 | self.c0().is_zero() && self.c1().is_zero() 39 | } 40 | } 41 | 42 | impl Cipher { 43 | pub fn c0(&self) -> C::Affine { 44 | self.0[0] 45 | } 46 | 47 | pub fn c1(&self) -> C::Affine { 48 | self.0[1] 49 | } 50 | 51 | pub fn check_encrypted_sum(&self, ciphers: &[Self]) -> bool { 52 | let ciphers_sum = ciphers 53 | .iter() 54 | .enumerate() 55 | .fold(Self::zero(), |acc, (i, c)| { 56 | acc + *c * shift_scalar(&C::ScalarField::one(), MAX_BITS * i) 57 | }); 58 | ciphers_sum == *self 59 | } 60 | } 61 | 62 | impl Add for Cipher { 63 | type Output = Self; 64 | fn add(self, rhs: Self) -> Self::Output { 65 | Self([ 66 | (self.c0() + rhs.c0()).into_affine(), 67 | (self.c1() + rhs.c1()).into_affine(), 68 | ]) 69 | } 70 | } 71 | 72 | impl Mul for Cipher { 73 | type Output = Self; 74 | fn mul(self, rhs: C::ScalarField) -> Self::Output { 75 | Self([ 76 | (self.c0() * rhs).into_affine(), 77 | (self.c1() * rhs).into_affine(), 78 | ]) 79 | } 80 | } 81 | 82 | impl EncryptionEngine for ExponentialElgamal { 83 | type EncryptionKey = C::Affine; 84 | type DecryptionKey = C::ScalarField; 85 | type Cipher = Cipher; 86 | type PlainText = C::ScalarField; 87 | 88 | fn encrypt( 89 | data: &Self::PlainText, 90 | key: &Self::EncryptionKey, 91 | rng: &mut R, 92 | ) -> Self::Cipher { 93 | let random_nonce = C::ScalarField::rand(rng); 94 | Self::encrypt_with_randomness(data, key, &random_nonce) 95 | } 96 | 97 | fn encrypt_with_randomness( 98 | data: &Self::PlainText, 99 | key: &Self::EncryptionKey, 100 | randomness: &Self::PlainText, 101 | ) -> Self::Cipher { 102 | // h^y 103 | let shared_secret = *key * randomness; 104 | // g^y 105 | let c1 = ::generator() * randomness; 106 | // g^m * h^y 107 | let c2 = ::generator() * data + shared_secret; 108 | Cipher([c1.into_affine(), c2.into_affine()]) 109 | } 110 | 111 | fn decrypt(cipher: Self::Cipher, key: &Self::DecryptionKey) -> Self::PlainText { 112 | let decrypted_exp = Self::decrypt_exp(cipher, key); 113 | Self::brute_force(decrypted_exp) 114 | } 115 | } 116 | 117 | impl ExponentialElgamal { 118 | pub fn decrypt_exp(cipher: Cipher, key: &C::ScalarField) -> C::Affine { 119 | let shared_secret = (cipher.c0() * key).into_affine(); 120 | // AffineRepr has to be converted into a Group element in order to perform subtraction but 121 | // I believe this is optimized away in release mode 122 | (cipher.c1().into() - shared_secret.into()).into_affine() 123 | } 124 | 125 | pub fn brute_force(decrypted: C::Affine) -> C::ScalarField { 126 | let max = C::ScalarField::from(u32::MAX); 127 | let mut exponent = C::ScalarField::zero(); 128 | 129 | while (::generator() * exponent).into_affine() != decrypted 130 | && exponent < max 131 | { 132 | exponent += C::ScalarField::one(); 133 | } 134 | exponent 135 | } 136 | } 137 | 138 | #[cfg(test)] 139 | mod test { 140 | use super::*; 141 | use crate::tests::{G1Affine, Scalar, TestCurve, N}; 142 | use ark_ec::pairing::Pairing; 143 | use ark_ec::{AffineRepr, CurveGroup}; 144 | use ark_std::{test_rng, UniformRand}; 145 | 146 | type Elgamal = ExponentialElgamal<::G1>; 147 | 148 | #[test] 149 | fn exponential_elgamal() { 150 | let rng = &mut test_rng(); 151 | let decryption_key = Scalar::rand(rng); 152 | let encryption_key = (G1Affine::generator() * decryption_key).into_affine(); 153 | 154 | // completeness 155 | let data = Scalar::from(12342526u32); 156 | let encrypted = Elgamal::encrypt(&data, &encryption_key, rng); 157 | let decrypted = Elgamal::decrypt_exp(encrypted, &decryption_key); 158 | assert_eq!(decrypted, (G1Affine::generator() * data).into_affine()); 159 | // soundness 160 | let data = Scalar::from(12342526u32); 161 | let invalid_decryption_key = decryption_key + Scalar::from(123u32); 162 | let encrypted = Elgamal::encrypt(&data, &encryption_key, rng); 163 | let decrypted = Elgamal::decrypt_exp(encrypted, &invalid_decryption_key); 164 | assert_ne!(decrypted, (G1Affine::generator() * data).into_affine()); 165 | 166 | // with brute force check 167 | let data = Scalar::from(12u32); 168 | let encrypted = Elgamal::encrypt(&data, &encryption_key, rng); 169 | let decrypted = Elgamal::decrypt(encrypted, &decryption_key); 170 | assert_eq!(decrypted, data); 171 | } 172 | 173 | #[test] 174 | fn elgamal_homomorphism() { 175 | let a = Scalar::from(16u8); 176 | let b = Scalar::from(10u8); 177 | let c = Scalar::from(100u8); 178 | let ra = Scalar::from(2u8); 179 | let rb = Scalar::from(20u8); 180 | let rc = Scalar::from(200u8); 181 | 182 | let decryption_key = Scalar::from(1234567); 183 | let encryption_key = (G1Affine::generator() * decryption_key).into_affine(); 184 | 185 | let ea = Elgamal::encrypt_with_randomness(&a, &encryption_key, &ra); 186 | let eb = Elgamal::encrypt_with_randomness(&b, &encryption_key, &rb); 187 | let ec = Elgamal::encrypt_with_randomness(&c, &encryption_key, &rc); 188 | 189 | let sum = a + b + c; 190 | let rsum = ra + rb + rc; 191 | let esum = ea + eb + ec; 192 | 193 | assert_eq!(esum.c0(), G1Affine::generator() * rsum); 194 | assert_eq!( 195 | esum.c1(), 196 | G1Affine::generator() * sum + encryption_key * rsum 197 | ); 198 | 199 | let ma = Scalar::from(3u8); 200 | let mb = Scalar::from(4u8); 201 | let mc = Scalar::from(5u8); 202 | 203 | let sum = ma * a + mb * b + mc * c; 204 | let rsum = ma * ra + mb * rb + mc * rc; 205 | let esum = ea * ma + eb * mb + ec * mc; 206 | 207 | assert_eq!(esum.c0(), G1Affine::generator() * rsum); 208 | assert_eq!( 209 | esum.c1(), 210 | G1Affine::generator() * sum + encryption_key * rsum 211 | ); 212 | } 213 | 214 | #[test] 215 | fn split_encryption() { 216 | let rng = &mut test_rng(); 217 | let scalar = Scalar::rand(rng); 218 | let split_scalar = SplitScalar::<{ N }, Scalar>::from(scalar); 219 | let secret = Scalar::rand(rng); 220 | let encryption_key = (G1Affine::generator() * secret).into_affine(); 221 | 222 | let (ciphers, randomness) = split_scalar.encrypt::(&encryption_key, rng); 223 | 224 | let cipher = Elgamal::encrypt_with_randomness(&scalar, &encryption_key, &randomness); 225 | 226 | assert!(cipher.check_encrypted_sum(&ciphers)); 227 | } 228 | } 229 | -------------------------------------------------------------------------------- /src/encrypt/elgamal/split_scalar.rs: -------------------------------------------------------------------------------- 1 | use super::utils::shift_scalar; 2 | use super::MAX_BITS; 3 | use crate::encrypt::EncryptionEngine; 4 | use ark_ff::fields::PrimeField; 5 | use ark_ff::BigInteger; 6 | use ark_std::rand::Rng; 7 | #[cfg(feature = "parallel")] 8 | use rayon::prelude::*; 9 | 10 | #[derive(Clone, Copy, Debug)] 11 | pub struct SplitScalar([S; N]); 12 | 13 | impl SplitScalar { 14 | pub fn new(inner: [S; N]) -> Self { 15 | Self(inner) 16 | } 17 | 18 | pub fn reconstruct(&self) -> S { 19 | sum_shifted(self.splits()) 20 | } 21 | 22 | pub fn encrypt( 23 | self, 24 | encryption_key: &E::EncryptionKey, 25 | rng: &mut R, 26 | ) -> ([E::Cipher; N], S) 27 | where 28 | E: EncryptionEngine, 29 | E::Cipher: ark_std::fmt::Debug, 30 | R: Rng, 31 | { 32 | let rands: Vec<S> = (0..N).map(|_| S::rand(rng)).collect(); 33 | let ciphers: Vec<E::Cipher> = self 34 | .0 35 | .iter() 36 | .zip(&rands) 37 | .map(|(s, r)| E::encrypt_with_randomness(s, encryption_key, r)) 38 | .collect(); 39 | 40 | let shifted_rand_sum = sum_shifted(&rands); 41 | 42 | // NOTE unwrap is fine because ciphers.len() is always N 43 | (ciphers.try_into().unwrap(), shifted_rand_sum) 44 | } 45 | 46 | pub fn splits(&self) -> &[S; N] { 47 | &self.0 48 | } 49 | } 50 | 51 | #[cfg(not(feature = "parallel"))] 52 | fn sum_shifted<S: PrimeField>(splits: &[S]) -> S { 53 | splits 54 | .iter() 55 | .enumerate() 56 | .fold(S::zero(), |acc, (i, s)| acc + shift_scalar(s, MAX_BITS * i)) 57 | } 58 | 59 | #[cfg(feature = "parallel")] 60 | fn sum_shifted<S: PrimeField>(splits: &[S]) -> S { 61 | splits 62 | .par_iter() 63 | .enumerate() 64 | .fold( 65 | || S::zero(), 66 | |acc, (i, s)| acc + shift_scalar(s, MAX_BITS * i), 67 | ) 68 | .sum() 69 | } 70 | 71 | impl<const N: usize, S: PrimeField> From<S> for SplitScalar<N, S> { 72 | fn from(scalar: S) -> Self { 73 | let scalar_le_bytes = scalar.into_bigint().to_bits_le(); 74 | let mut output = [S::zero(); N]; 75 | 76 | for (i, chunk) in scalar_le_bytes.chunks(MAX_BITS).enumerate() { 77 | let split = S::from_bigint(<S::BigInt as BigInteger>::from_bits_le(chunk)) 78 | .expect("should not fail"); 79 | output[i] = split; 80 | } 81 | Self::new(output) 82 | } 83 | } 84 | 85 | #[cfg(test)] 86 | mod test { 87 | use super::*; 88 | use crate::tests::{G1Affine, Scalar, TestCurve, N}; 89 | use ark_ec::pairing::Pairing; 90 | use ark_ec::{AffineRepr, CurveGroup}; 91 | use ark_std::{test_rng, UniformRand, Zero}; 92 | 93 | type Elgamal = super::super::ExponentialElgamal<<TestCurve as Pairing>::G1>; 94 | 95 | #[test] 96 | fn scalar_splitting() { 97 | let scalar = Scalar::zero(); 98 | let split_scalar = SplitScalar::<{ N }, Scalar>::from(scalar); 99 | let reconstructed_scalar = split_scalar.reconstruct(); 100 | assert_eq!(scalar, reconstructed_scalar); 101 | 102 | let rng = &mut test_rng(); 103 | let max_scalar = Scalar::from(u32::MAX); 104 | for _ in 0..10 { 105 | let scalar = Scalar::rand(rng); 106 | let split_scalar = SplitScalar::<{ N }, Scalar>::from(scalar); 107 | for split in split_scalar.splits() { 108 | assert!(split <= &max_scalar); 109 | } 110 | let reconstructed_scalar = split_scalar.reconstruct(); 111 | assert_eq!(scalar, reconstructed_scalar); 112 | } 113 | } 114 | 115 | #[test] 116 | fn encryption() { 117 | let rng = &mut test_rng(); 118 | let encryption_pk = (G1Affine::generator() * Scalar::rand(rng)).into_affine(); 119 | let scalar = Scalar::rand(rng); 120 | let split_scalar = SplitScalar::<{ N }, Scalar>::from(scalar); 121 | 122 | let (short_ciphers, elgamal_r) = split_scalar.encrypt::<Elgamal, _>(&encryption_pk, rng); 123 | let long_cipher = <Elgamal as EncryptionEngine>::encrypt_with_randomness( 124 | &scalar, 125 | &encryption_pk, 126 | &elgamal_r, 127 | ); 128 | 129 | assert!(long_cipher.check_encrypted_sum(&short_ciphers)); 130 | } 131 | } 132 | -------------------------------------------------------------------------------- /src/encrypt/elgamal/utils.rs: -------------------------------------------------------------------------------- 1 | use ark_ff::fields::PrimeField; 2 | use ark_ff::BigInteger; 3 | 4 | pub fn shift_scalar<S: PrimeField>(scalar: &S, by: usize) -> S { 5 | let mut bigint = S::one().into_bigint(); 6 | bigint.muln(by as u32); 7 | *scalar * S::from_bigint(bigint).unwrap() 8 | } 9 | 10 | #[cfg(test)] 11 | mod test { 12 | use super::*; 13 | use ark_bls12_381::Fr; 14 | use ark_std::{One, Zero}; 15 | 16 | #[test] 17 | fn scalar_shifting() { 18 | let scalar = Fr::zero(); 19 | assert_eq!(shift_scalar(&scalar, 32), Fr::zero()); 20 | 21 | let scalar = Fr::one(); 22 | assert_eq!( 23 | shift_scalar(&scalar, 32), 24 | Fr::from(u64::from(u32::MAX) + 1u64) 25 | ); 26 | 27 | // shifting with overflow 28 | // according to the docs, overflow is 29 | // ignored 30 | let scalar = Fr::one(); 31 | assert_eq!(shift_scalar(&scalar, u32::MAX as usize), Fr::zero()); 32 | } 33 | } 34 | -------------------------------------------------------------------------------- /src/encrypt/mod.rs: -------------------------------------------------------------------------------- 1 | pub mod elgamal; 2 | 3 | use ark_std::rand::Rng; 4 | 5 | pub trait EncryptionEngine { 6 | type EncryptionKey; 7 | type DecryptionKey; 8 | type Cipher; 9 | type PlainText; 10 | fn encrypt<R: Rng>( 11 | data: &Self::PlainText, 12 | key: &Self::EncryptionKey, 13 | rng: &mut R, 14 | ) -> Self::Cipher; 15 | fn encrypt_with_randomness( 16 | data: &Self::PlainText, 17 | key: &Self::EncryptionKey, 18 | randomness: &Self::PlainText, 19 | ) -> Self::Cipher; 20 | fn decrypt(cipher: Self::Cipher, key: &Self::DecryptionKey) -> Self::PlainText; 21 | } 22 | -------------------------------------------------------------------------------- /src/hash.rs: -------------------------------------------------------------------------------- 1 | use ark_ff::PrimeField; 2 | use ark_serialize::CanonicalSerialize; 3 | use ark_std::marker::PhantomData; 4 | use digest::{Digest, Output}; 5 | 6 | #[derive(Clone, Debug)] 7 | pub struct Hasher<D> { 8 | data: Vec<u8>, 9 | _digest: PhantomData<D>, 10 | } 11 | 12 | impl<D> Default for Hasher<D> { 13 | fn default() -> Self { 14 | Self { 15 | data: Vec::new(), 16 | _digest: PhantomData, 17 | } 18 | } 19 | } 20 | 21 | impl<D: Digest> Hasher<D> { 22 | pub fn new() -> Self { 23 | Self::default() 24 | } 25 | 26 | pub fn update<T: CanonicalSerialize>(&mut self, input: &T) { 27 | input 28 | .serialize_compressed(&mut self.data) 29 | .expect("should not fail"); 30 | } 31 | 32 | pub fn finalize(self) -> Output<D> { 33 | D::digest(self.data) 34 | } 35 | 36 | pub fn next_scalar<S: PrimeField>(&mut self, label: &[u8]) -> S { 37 | self.data.extend_from_slice(label); 38 | let output = D::digest(&self.data); 39 | S::from_le_bytes_mod_order(&output) 40 | } 41 | } 42 | -------------------------------------------------------------------------------- /src/lib.rs: -------------------------------------------------------------------------------- 1 | #![deny(clippy::all)] 2 | #![deny(clippy::dbg_macro)] 3 | #![deny(unused_crate_dependencies)] 4 | 5 | pub mod adaptor_sig; 6 | pub mod commit; 7 | pub mod dleq; 8 | pub mod encrypt; 9 | pub mod hash; 10 | pub mod range_proof; 11 | #[cfg(test)] 12 | mod tests; 13 | pub mod veck; 14 | 15 | use thiserror::Error; 16 | 17 | #[derive(Error, Debug, PartialEq)] 18 | pub enum Error { 19 | #[error("couldn't generate valid FFT domain of size {0}")] 20 | InvalidFftDomain(usize), 21 | #[error(transparent)] 22 | RangeProof(#[from] range_proof::Error), 23 | #[error(transparent)] 24 | KzgElgamalProofError(#[from] veck::kzg::elgamal::Error), 25 | #[error(transparent)] 26 | KzgPaillierProofError(#[from] veck::kzg::paillier::Error), 27 | } 28 | -------------------------------------------------------------------------------- /src/range_proof/mod.rs: -------------------------------------------------------------------------------- 1 | //! This crate contains a proof-of-concept implementation of the 2 | //! [Boneh-Fisch-Gabizon-Williamson](https://hackmd.io/@dabo/B1U4kx8XI) range proof. 3 | //! 4 | //! The protocol relies on KZG commitments, thus it fits our KZG-based protocols perfectly. Further 5 | //! discussion of the proof can be found 6 | //! [here](https://decentralizedthoughts.github.io/2020-03-03-range-proofs-from-polynomial-commitments-reexplained/). 7 | //! 8 | //! This implementation is a modernized/updated version of the code found 9 | //! [here](https://github.com/roynalnaruto/range_proof). 10 | mod poly; 11 | mod utils; 12 | 13 | use crate::commit::kzg::{Kzg, Powers}; 14 | use crate::hash::Hasher; 15 | use crate::Error as CrateError; 16 | use ark_ec::pairing::Pairing; 17 | use ark_ec::{AffineRepr, CurveGroup}; 18 | use ark_poly::{EvaluationDomain, GeneralEvaluationDomain, Polynomial}; 19 | use ark_std::marker::PhantomData; 20 | use ark_std::rand::Rng; 21 | use ark_std::UniformRand; 22 | use digest::Digest; 23 | use thiserror::Error as ErrorT; 24 | 25 | #[derive(ErrorT, Debug, PartialEq)] 26 | pub enum Error { 27 | #[error("aggregated witness pairings are not equal")] 28 | AggregateWitnessCheckFailed, 29 | #[error("shifted witness pairings are not equal")] 30 | ShiftedWitnessCheckFailed, 31 | #[error("input value is greater than the upper range bound")] 32 | InputOutOfBounds, 33 | #[error("polynomial is nonzero")] 34 | ExpectedZeroPolynomial, 35 | } 36 | 37 | const PROOF_DOMAIN_SEP: &[u8] = b"fde range proof"; 38 | 39 | #[derive(Clone, Copy, Debug)] 40 | pub struct Evaluations<S> { 41 | pub g: S, 42 | pub g_omega: S, 43 | pub w_cap: S, 44 | } 45 | 46 | #[derive(Clone, Copy, Debug)] 47 | pub struct Commitments<C: Pairing> { 48 | pub f: C::G1Affine, 49 | pub g: C::G1Affine, 50 | pub q: C::G1Affine, 51 | } 52 | 53 | #[derive(Clone, Copy, Debug)] 54 | pub struct Proofs<C: Pairing> { 55 | pub aggregate: C::G1Affine, 56 | pub shifted: C::G1Affine, 57 | } 58 | 59 | #[derive(Clone, Copy, Debug)] 60 | pub struct RangeProof<C: Pairing, D> { 61 | pub evaluations: Evaluations<C::ScalarField>, 62 | pub commitments: Commitments<C>, 63 | pub proofs: Proofs<C>, 64 | _digest: PhantomData<D>, 65 | } 66 | 67 | impl<C: Pairing, D: Digest> RangeProof<C, D> { 68 | // prove 0 <= z < 2^n 69 | pub fn new<R: Rng>( 70 | z: C::ScalarField, 71 | n: usize, 72 | powers: &Powers<C>, 73 | rng: &mut R, 74 | ) -> Result<Self, CrateError> { 75 | let domain = GeneralEvaluationDomain::<C::ScalarField>::new(n) 76 | .ok_or(CrateError::InvalidFftDomain(n))?; 77 | let domain_2n = GeneralEvaluationDomain::<C::ScalarField>::new(2 * n) 78 | .ok_or(CrateError::InvalidFftDomain(2 * n))?; 79 | 80 | // random scalars 81 | let r = C::ScalarField::rand(rng); 82 | let alpha = C::ScalarField::rand(rng); 83 | let beta = C::ScalarField::rand(rng); 84 | 85 | // compute f and g polynomials and their commitments 86 | let f_poly = poly::f(&domain, z, r); 87 | let g_poly = poly::g(&domain, z, alpha, beta); 88 | let f_commitment = powers.commit_g1(&f_poly); 89 | let g_commitment = powers.commit_g1(&g_poly); 90 | 91 | // compute challenges 92 | let mut hasher = Hasher::<D>::new(); 93 | hasher.update(&PROOF_DOMAIN_SEP); 94 | hasher.update(&n.to_le_bytes()); 95 | hasher.update(&domain.group_gen()); 96 | hasher.update(&f_commitment); 97 | hasher.update(&g_commitment); 98 | 99 | let tau = hasher.next_scalar(b"tau"); 100 | let rho = hasher.next_scalar(b"rho"); 101 | let aggregation_challenge = hasher.next_scalar(b"aggregation_challenge"); 102 | 103 | // aggregate w1, w2 and w3 to compute quotient polynomial 104 | let (w1_poly, w2_poly) = poly::w1_w2(&domain, &f_poly, &g_poly)?; 105 | let w3_poly = poly::w3(&domain, &domain_2n, &g_poly)?; 106 | let q_poly = poly::quotient(&domain, &w1_poly, &w2_poly, &w3_poly, tau)?; 107 | let q_commitment = powers.commit_g1(&q_poly); 108 | 109 | let rho_omega = rho * domain.group_gen(); 110 | // evaluate g at rho 111 | let g_eval = g_poly.evaluate(&rho); 112 | // evaluate g at `rho * omega` 113 | let g_omega_eval = g_poly.evaluate(&rho_omega); 114 | 115 | // compute evaluation of w_cap at ρ 116 | let w_cap_poly = poly::w_cap(&domain, &f_poly, &q_poly, rho); 117 | let w_cap_eval = w_cap_poly.evaluate(&rho); 118 | 119 | // compute witness for g(X) at ρw 120 | let shifted_witness_poly = Kzg::<C>::witness(&g_poly, rho_omega); 121 | let shifted_proof = powers.commit_g1(&shifted_witness_poly); 122 | 123 | // compute aggregate witness for 124 | // g(X) at ρ, f(X) at ρ, w_cap(X) at ρ 125 | let aggregate_witness_poly = 126 | Kzg::<C>::aggregate_witness(&[g_poly, w_cap_poly], rho, aggregation_challenge); 127 | let aggregate_proof = powers.commit_g1(&aggregate_witness_poly); 128 | 129 | let evaluations = Evaluations { 130 | g: g_eval, 131 | g_omega: g_omega_eval, 132 | w_cap: w_cap_eval, 133 | }; 134 | 135 | let commitments = Commitments { 136 | f: f_commitment.into_affine(), 137 | g: g_commitment.into_affine(), 138 | q: q_commitment.into_affine(), 139 | }; 140 | 141 | let proofs = Proofs { 142 | aggregate: aggregate_proof.into_affine(), 143 | shifted: shifted_proof.into_affine(), 144 | }; 145 | 146 | Ok(Self { 147 | evaluations, 148 | commitments, 149 | proofs, 150 | _digest: PhantomData, 151 | }) 152 | } 153 | 154 | pub fn verify(&self, n: usize, powers: &Powers<C>) -> Result<(), CrateError> { 155 | let domain = GeneralEvaluationDomain::<C::ScalarField>::new(n) 156 | .ok_or(CrateError::InvalidFftDomain(n))?; 157 | 158 | let mut hasher = Hasher::<D>::new(); 159 | hasher.update(&PROOF_DOMAIN_SEP); 160 | hasher.update(&n.to_le_bytes()); 161 | hasher.update(&domain.group_gen()); 162 | hasher.update(&self.commitments.f); 163 | hasher.update(&self.commitments.g); 164 | 165 | let tau = hasher.next_scalar(b"tau"); 166 | let rho = hasher.next_scalar(b"rho"); 167 | let aggregation_challenge: C::ScalarField = hasher.next_scalar(b"aggregation_challenge"); 168 | 169 | // calculate w_cap_commitment 170 | let w_cap_commitment = 171 | utils::w_cap::<C::G1>(domain.size(), self.commitments.f, self.commitments.q, rho); 172 | 173 | // calculate w2(ρ) and w3(ρ) 174 | let sum = utils::w1_w2_w3_evals_sum( 175 | &domain, 176 | self.evaluations.g, 177 | self.evaluations.g_omega, 178 | rho, 179 | tau, 180 | ); 181 | // calculate w(ρ) that should zero since w(X) is after all a zero polynomial 182 | if sum != self.evaluations.w_cap { 183 | return Err(Error::ExpectedZeroPolynomial.into()); 184 | } 185 | 186 | // check aggregate witness commitment 187 | let aggregate_poly_commitment = utils::aggregate( 188 | &[ 189 | self.commitments.g.into_group(), 190 | w_cap_commitment.into_group(), 191 | ], 192 | aggregation_challenge, 193 | ); 194 | let aggregate_value = utils::aggregate( 195 | &[self.evaluations.g, self.evaluations.w_cap], 196 | aggregation_challenge, 197 | ); 198 | let aggregation_kzg_check = Kzg::verify_scalar( 199 | self.proofs.aggregate, 200 | aggregate_poly_commitment.into_affine(), 201 | rho, 202 | aggregate_value, 203 | powers, 204 | ); 205 | 206 | // check shifted witness commitment 207 | let rho_omega = rho * domain.group_gen(); 208 | let shifted_kzg_check = Kzg::verify_scalar( 209 | self.proofs.shifted, 210 | self.commitments.g, 211 | rho_omega, 212 | self.evaluations.g_omega, 213 | powers, 214 | ); 215 | 216 | if !aggregation_kzg_check { 217 | Err(Error::AggregateWitnessCheckFailed.into()) 218 | } else if !shifted_kzg_check { 219 | Err(Error::ShiftedWitnessCheckFailed.into()) 220 | } else { 221 | Ok(()) 222 | } 223 | } 224 | } 225 | 226 | #[cfg(test)] 227 | mod test { 228 | use super::*; 229 | use crate::commit::kzg::Powers; 230 | use crate::tests::{Scalar, TestCurve, TestHash}; 231 | use crate::Error as CrateError; 232 | use ark_std::{test_rng, UniformRand}; 233 | 234 | const LOG_2_UPPER_BOUND: usize = 8; // 2^8 235 | 236 | #[test] 237 | fn range_proof_success() { 238 | // KZG setup simulation 239 | let rng = &mut test_rng(); 240 | let tau = Scalar::rand(rng); // "secret" tau 241 | let powers = Powers::<TestCurve>::unsafe_setup(tau, 4 * LOG_2_UPPER_BOUND); 242 | 243 | let z = Scalar::from(100u32); 244 | let proof = 245 | RangeProof::<TestCurve, TestHash>::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap(); 246 | assert!(proof.verify(LOG_2_UPPER_BOUND, &powers).is_ok()); 247 | 248 | let z = Scalar::from(255u32); 249 | let proof = 250 | RangeProof::<TestCurve, TestHash>::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap(); 251 | assert!(proof.verify(LOG_2_UPPER_BOUND, &powers).is_ok()); 252 | } 253 | 254 | #[test] 255 | fn range_proof_with_invalid_size_fails() { 256 | // KZG setup simulation 257 | let rng = &mut test_rng(); 258 | let tau = Scalar::rand(rng); // "secret" tau 259 | let powers = Powers::<TestCurve>::unsafe_setup(tau, 4 * LOG_2_UPPER_BOUND); 260 | 261 | let z = Scalar::from(100u32); 262 | let proof = 263 | RangeProof::<TestCurve, TestHash>::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap(); 264 | assert_eq!( 265 | proof.verify(LOG_2_UPPER_BOUND - 1, &powers), 266 | Err(CrateError::RangeProof(Error::ExpectedZeroPolynomial)) 267 | ); 268 | } 269 | 270 | #[test] 271 | fn range_proof_with_too_large_z_fails_1() { 272 | // KZG setup simulation 273 | let rng = &mut test_rng(); 274 | let tau = Scalar::rand(rng); // "secret" tau 275 | let powers = Powers::<TestCurve>::unsafe_setup(tau, 4 * LOG_2_UPPER_BOUND); 276 | 277 | let z = Scalar::from(256u32); 278 | assert_eq!( 279 | RangeProof::<TestCurve, TestHash>::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap_err(), 280 | CrateError::RangeProof(Error::ExpectedZeroPolynomial) 281 | ); 282 | } 283 | 284 | #[test] 285 | fn range_proof_with_too_large_z_fails_2() { 286 | // KZG setup simulation 287 | let rng = &mut test_rng(); 288 | let tau = Scalar::rand(rng); // "secret" tau 289 | let powers = Powers::<TestCurve>::unsafe_setup(tau, 4 * LOG_2_UPPER_BOUND); 290 | 291 | let z = Scalar::from(300u32); 292 | assert_eq!( 293 | RangeProof::<TestCurve, TestHash>::new(z, LOG_2_UPPER_BOUND, &powers, rng).unwrap_err(), 294 | CrateError::RangeProof(Error::ExpectedZeroPolynomial) 295 | ); 296 | } 297 | } 298 | -------------------------------------------------------------------------------- /src/range_proof/poly.rs: -------------------------------------------------------------------------------- 1 | use super::Error; 2 | use crate::Error as CrateError; 3 | use ark_ff::{BigInteger, PrimeField}; 4 | use ark_poly::univariate::DensePolynomial; 5 | use ark_poly::{DenseUVPolynomial, EvaluationDomain, GeneralEvaluationDomain}; 6 | use ark_std::Zero; 7 | 8 | pub fn f<S: PrimeField>(domain: &GeneralEvaluationDomain<S>, z: S, r: S) -> DensePolynomial<S> { 9 | // f is a linear polynomial: f(1) = z 10 | DensePolynomial::from_coefficients_vec(domain.ifft(&[z, r])) 11 | } 12 | 13 | pub fn g<S: PrimeField>( 14 | domain: &GeneralEvaluationDomain<S>, 15 | z: S, 16 | alpha: S, 17 | beta: S, 18 | ) -> DensePolynomial<S> { 19 | // get bits for z -> consider only the first `n` bits 20 | let size = domain.size(); 21 | let z_bits = &z.into_bigint().to_bits_le()[0..size]; 22 | let mut evaluations: Vec<S> = vec![S::zero(); size]; 23 | 24 | // take the first evaluation point, i.e. (n-1)th bit of z 25 | evaluations[size - 1] = S::from(z_bits[size - 1]); 26 | 27 | // for the rest of bits (n-2 .. 0) 28 | // g_i = 2* g_(i+1) + z_i 29 | z_bits 30 | .iter() 31 | .enumerate() 32 | .rev() 33 | .skip(1) 34 | .for_each(|(i, &bit)| { 35 | evaluations[i] = S::from(2u8) * evaluations[i + 1] + S::from(bit as u8); 36 | }); 37 | 38 | // compute g 39 | let g_poly = DensePolynomial::from_coefficients_vec(domain.ifft(&evaluations)); 40 | 41 | // extended domain 42 | let domain_ext = GeneralEvaluationDomain::<S>::new(size + 1).expect("valid domain"); 43 | 44 | // Map the original g_poly to domain(n+1). Add random values alpha and beta as evaluations of g 45 | // at all even indices, g_evals[2k] matches the evaluation at some original root of unity. 46 | // Hence only update two odd indices with alpha and beta this makes g evaluate to the expected 47 | // evaluations at all roots of unity of domain size `n`, but makes is a different polynomial 48 | let mut g_evals = domain_ext.fft(&g_poly); 49 | g_evals[1] = alpha; 50 | g_evals[3] = beta; 51 | 52 | DensePolynomial::from_coefficients_vec(domain_ext.ifft(&g_evals)) 53 | } 54 | 55 | pub fn w1_w2<S: PrimeField>( 56 | domain: &GeneralEvaluationDomain<S>, 57 | f_poly: &DensePolynomial<S>, 58 | g_poly: &DensePolynomial<S>, 59 | ) -> Result<(DensePolynomial<S>, DensePolynomial<S>), CrateError> { 60 | let one = S::one(); 61 | let w_n_minus_1 = domain 62 | .elements() 63 | .last() 64 | .ok_or(CrateError::InvalidFftDomain(0))?; 65 | 66 | // polynomial: P(x) = x - w^(n-1) 67 | let x_minus_w_n_minus_1_poly = DensePolynomial::from_coefficients_slice(&[-w_n_minus_1, one]); 68 | 69 | // polynomial: P(x) = x^n - 1 70 | let x_n_minus_1_poly = DensePolynomial::from(domain.vanishing_polynomial()); 71 | 72 | // polynomial: P(x) = x - 1 73 | let x_minus_1_poly = DensePolynomial::from_coefficients_slice(&[-one, one]); 74 | 75 | let g_minus_f_poly = g_poly - f_poly; 76 | let w1_poly = &(&g_minus_f_poly * &x_n_minus_1_poly) / &x_minus_1_poly; 77 | 78 | // polynomial: P(x) = 1 79 | let one_poly = DensePolynomial::from_coefficients_slice(&[one]); 80 | let one_minus_g_poly = &one_poly - g_poly; 81 | let w2_poly = &(&(g_poly * &one_minus_g_poly) * &x_n_minus_1_poly) / &x_minus_w_n_minus_1_poly; 82 | 83 | Ok((w1_poly, w2_poly)) 84 | } 85 | 86 | pub fn w3<S: PrimeField>( 87 | domain: &GeneralEvaluationDomain<S>, 88 | domain_2n: &GeneralEvaluationDomain<S>, 89 | g_poly: &DensePolynomial<S>, 90 | ) -> Result<DensePolynomial<S>, CrateError> { 91 | // w3: [g(X) - 2g(Xw)] * [1 - g(X) + 2g(Xw)] * [X - w^(n-1)] 92 | // degree of g = n - 1 93 | // degree of w3 = (2n - 1) + (2n - 1) + 1 = 4n - 1 94 | // the new domain can be of size 4n 95 | let domain_4n = GeneralEvaluationDomain::<S>::new(2 * domain_2n.size()) 96 | .ok_or(CrateError::InvalidFftDomain(2 * domain_2n.size()))?; 97 | 98 | // find evaluations of g in the new domain 99 | let mut g_evals = domain_4n.fft(g_poly); 100 | 101 | // since we have doubled the domain size, the roots of unity of the new domain will also occur 102 | // among the roots of unity of the original domain. hence, if g(X) <- g_evals[i] then g(Xw) <- 103 | // g_evals[i+4] 104 | g_evals.push(g_evals[0]); 105 | g_evals.push(g_evals[1]); 106 | g_evals.push(g_evals[2]); 107 | g_evals.push(g_evals[3]); 108 | 109 | // calculate evaluations of w3 110 | let w_n_minus_1 = domain 111 | .elements() 112 | .last() 113 | .ok_or(CrateError::InvalidFftDomain(0))?; 114 | let two = S::from(2u8); 115 | let w3_evals: Vec<S> = domain_4n 116 | .elements() 117 | .enumerate() 118 | .map(|(i, x_i)| { 119 | let part_a = g_evals[i] - (two * g_evals[i + 4]); 120 | let part_b = S::one() - g_evals[i] + (two * g_evals[i + 4]); 121 | let part_c = x_i - w_n_minus_1; 122 | part_a * part_b * part_c 123 | }) 124 | .collect(); 125 | 126 | Ok(DensePolynomial::from_coefficients_vec( 127 | domain_4n.ifft(&w3_evals), 128 | )) 129 | } 130 | 131 | pub fn w_cap<S: PrimeField>( 132 | domain: &GeneralEvaluationDomain<S>, 133 | f_poly: &DensePolynomial<S>, 134 | q_poly: &DensePolynomial<S>, 135 | rho: S, 136 | ) -> DensePolynomial<S> { 137 | let (rho_1, rho_2) = super::utils::rho_relations(domain.size(), rho); 138 | let rho_poly_1 = DensePolynomial::from_coefficients_slice(&[rho_1]); 139 | let rho_poly_2 = DensePolynomial::from_coefficients_slice(&[rho_2]); 140 | &(f_poly * &rho_poly_1) + &(q_poly * &rho_poly_2) 141 | } 142 | 143 | pub fn quotient<S: PrimeField>( 144 | domain: &GeneralEvaluationDomain<S>, 145 | w1_poly: &DensePolynomial<S>, 146 | w2_poly: &DensePolynomial<S>, 147 | w3_poly: &DensePolynomial<S>, 148 | tau: S, 149 | ) -> Result<DensePolynomial<S>, CrateError> { 150 | // find linear combination of w1, w2, w3 151 | let lc = w1_poly + &(w2_poly * tau) + w3_poly * tau.square(); 152 | let (quotient_poly, rem) = lc 153 | .divide_by_vanishing_poly(*domain) 154 | .ok_or(CrateError::InvalidFftDomain(domain.size()))?; 155 | // since the linear combination should also satisfy all roots of unity, q_rem should be a zero 156 | // polynomial 157 | if !rem.is_zero() { 158 | Err(Error::ExpectedZeroPolynomial.into()) 159 | } else { 160 | Ok(quotient_poly) 161 | } 162 | } 163 | 164 | #[cfg(test)] 165 | mod test { 166 | use crate::commit::kzg::Powers; 167 | use crate::tests::{Scalar, TestCurve}; 168 | use ark_ec::pairing::Pairing; 169 | use ark_ec::CurveGroup; 170 | use ark_ff::{Field, PrimeField}; 171 | use ark_poly::univariate::DensePolynomial; 172 | use ark_poly::{DenseUVPolynomial, EvaluationDomain, GeneralEvaluationDomain, Polynomial}; 173 | use ark_std::{test_rng, UniformRand}; 174 | use ark_std::{One, Zero}; 175 | 176 | fn w2_w3_parts<S: PrimeField>( 177 | w2: &DensePolynomial<S>, 178 | w3: &DensePolynomial<S>, 179 | tau: S, 180 | ) -> (DensePolynomial<S>, DensePolynomial<S>) { 181 | (w2 * tau, w3 * tau.square()) 182 | } 183 | 184 | fn w1_part<S: PrimeField>( 185 | domain: &GeneralEvaluationDomain<S>, 186 | g_poly: &DensePolynomial<S>, 187 | ) -> DensePolynomial<S> { 188 | let one = S::one(); 189 | let divisor = DensePolynomial::<S>::from_coefficients_slice(&[-one, one]); 190 | &g_poly.mul_by_vanishing_poly(*domain) / &divisor 191 | } 192 | 193 | #[test] 194 | fn compute_f_poly_success() { 195 | let rng = &mut test_rng(); 196 | let n = 8usize; 197 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 198 | let z = Scalar::from(2u8); 199 | let r = Scalar::from(4u8); 200 | let f_poly = super::f(&domain, z, r); 201 | 202 | let rho = Scalar::rand(rng); 203 | 204 | assert_eq!(f_poly.evaluate(&Scalar::one()), z); 205 | assert_eq!(f_poly.evaluate(&domain.group_gen()), r); 206 | assert_ne!(f_poly.evaluate(&rho), z); 207 | assert_ne!(f_poly.evaluate(&rho), r); 208 | } 209 | #[test] 210 | fn compute_g_poly_success() { 211 | let rng = &mut test_rng(); 212 | // n = 8, 2^n = 256, 0 <= z < 2^n degree of polynomial should be (n - 1) it should also 213 | // evaluate to `z` at x = 1 214 | let n = 8usize; 215 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 216 | let z = Scalar::from(100u8); 217 | 218 | let alpha = Scalar::rand(rng); 219 | let beta = Scalar::rand(rng); 220 | let g_poly = super::g(&domain, z, alpha, beta); 221 | assert_eq!(g_poly.degree(), 2 * n - 1); 222 | assert_eq!(g_poly.evaluate(&Scalar::one()), z); 223 | 224 | // n2 = 4, 2^n2 = 16, 0 <= z < 2^n2 degree of polynomial should be (n2 - 1) it should also 225 | // evaluate to `z2` at x = 1 226 | let n = 8usize; 227 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 228 | let z = Scalar::from(13u8); 229 | 230 | let alpha = Scalar::rand(rng); 231 | let beta = Scalar::rand(rng); 232 | let g_poly = super::g(&domain, z, alpha, beta); 233 | assert_eq!(g_poly.degree(), 2 * n - 1); 234 | assert_eq!(g_poly.evaluate(&Scalar::one()), z); 235 | } 236 | 237 | #[test] 238 | fn compute_w1_w2_polys_success() { 239 | let rng = &mut test_rng(); 240 | 241 | let n = 8usize; 242 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 243 | 244 | let one = Scalar::one(); 245 | let zero = Scalar::zero(); 246 | let r = Scalar::rand(rng); 247 | let alpha = Scalar::rand(rng); 248 | let beta = Scalar::rand(rng); 249 | let z = Scalar::from(92u8); 250 | let f_poly = super::f(&domain, z, r); 251 | let g_poly = super::g(&domain, z, alpha, beta); 252 | 253 | let (w1_poly, w2_poly) = super::w1_w2(&domain, &f_poly, &g_poly).unwrap(); 254 | 255 | // both w1 and w2 should evaluate to 0 at x = 1 256 | assert_eq!(w1_poly.evaluate(&one), zero); 257 | assert_eq!(w2_poly.evaluate(&one), zero); 258 | 259 | // both w1 and w2 should evaluate to 0 at all roots of unity 260 | for root in domain.elements() { 261 | assert_eq!(w1_poly.evaluate(&root), zero); 262 | assert_eq!(w2_poly.evaluate(&root), zero); 263 | } 264 | 265 | let n_as_ref = Scalar::from(n as u8).into_bigint(); 266 | // evaluate w1 at a random field element 267 | let r = Scalar::rand(rng); 268 | let part_a = g_poly.evaluate(&r); 269 | let part_b = f_poly.evaluate(&r); 270 | let part_c = (r.pow(n_as_ref) - one) / (r - one); 271 | let w1_expected = (part_a - part_b) * part_c; 272 | assert_eq!(w1_poly.evaluate(&r), w1_expected); 273 | 274 | // evaluate w2 at a random field element 275 | let w_n_minus_1 = domain.elements().last().unwrap(); 276 | let r = Scalar::rand(rng); 277 | let part_a = g_poly.evaluate(&r); 278 | let part_b = one - part_a; 279 | let part_c = (r.pow(n_as_ref) - one) / (r - w_n_minus_1); 280 | let w2_expected = part_a * part_b * part_c; 281 | assert_eq!(w2_poly.evaluate(&r), w2_expected); 282 | } 283 | 284 | #[test] 285 | fn compute_w3_poly_success() { 286 | let rng = &mut test_rng(); 287 | 288 | let n = 8usize; 289 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 290 | let domain_2n = GeneralEvaluationDomain::<Scalar>::new(2 * n).unwrap(); 291 | 292 | let one = Scalar::one(); 293 | let two = Scalar::from(2u8); 294 | 295 | let z = Scalar::from(83u8); 296 | let alpha = Scalar::rand(rng); 297 | let beta = Scalar::rand(rng); 298 | let g_poly = super::g(&domain, z, alpha, beta); 299 | 300 | let w3_poly = super::w3(&domain, &domain_2n, &g_poly).unwrap(); 301 | 302 | // w3 should evaluate to 0 at all roots of unity for original domain 303 | for root in domain.elements() { 304 | assert!(w3_poly.evaluate(&root).is_zero()); 305 | } 306 | 307 | // w3 degree should be 4n - 1 308 | assert_eq!(w3_poly.degree(), 4 * domain.size() - 1); 309 | 310 | // evaluate w3 at a random field element 311 | let w_n_minus_1 = domain.elements().last().unwrap(); 312 | let r = Scalar::rand(rng); 313 | let part_a = g_poly.evaluate(&r) - two * g_poly.evaluate(&(r * domain.group_gen())); 314 | let part_b = one - g_poly.evaluate(&r) + two * g_poly.evaluate(&(r * domain.group_gen())); 315 | let part_c = r - w_n_minus_1; 316 | let w3_expected = part_a * part_b * part_c; 317 | assert_eq!(w3_poly.evaluate(&r), w3_expected); 318 | 319 | // evaluate w3 at another random field element 320 | let r = Scalar::rand(rng); 321 | let part_a = g_poly.evaluate(&r) - two * g_poly.evaluate(&(r * domain.group_gen())); 322 | let part_b = one - g_poly.evaluate(&r) + two * g_poly.evaluate(&(r * domain.group_gen())); 323 | let part_c = r - w_n_minus_1; 324 | let w3_expected = part_a * part_b * part_c; 325 | assert_eq!(w3_poly.evaluate(&r), w3_expected); 326 | } 327 | 328 | #[test] 329 | fn compute_w_cap_poly_success() { 330 | let rng = &mut test_rng(); 331 | 332 | // domain setup 333 | let n = 8usize; 334 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 335 | let domain_2n = GeneralEvaluationDomain::<Scalar>::new(2 * n).unwrap(); 336 | // KZG setup 337 | let tau = Scalar::rand(rng); // "secret" tau 338 | let powers = Powers::<TestCurve>::unsafe_setup(tau, 4 * n); 339 | 340 | // random numbers 341 | let r = Scalar::rand(rng); 342 | let t = Scalar::rand(rng); 343 | let rho = Scalar::rand(rng); 344 | let alpha = Scalar::rand(rng); 345 | let beta = Scalar::rand(rng); 346 | 347 | // compute polynomials 348 | let z = Scalar::from(68u8); 349 | let f_poly = super::f(&domain, z, r); 350 | let g_poly = super::g(&domain, z, alpha, beta); 351 | let (w1_poly, w2_poly) = super::w1_w2(&domain, &f_poly, &g_poly).unwrap(); 352 | let w3_poly = super::w3(&domain, &domain_2n, &g_poly).unwrap(); 353 | let q_poly = super::quotient(&domain, &w1_poly, &w2_poly, &w3_poly, t).unwrap(); 354 | let w_cap_poly = super::w_cap(&domain, &f_poly, &q_poly, rho); 355 | 356 | // compute commitments 357 | let f_commitment = powers.commit_g1(&f_poly).into_affine(); 358 | let q_commitment = powers.commit_g1(&q_poly).into_affine(); 359 | let w_cap_commitment_expected = powers.commit_g1(&w_cap_poly); 360 | 361 | // calculate w_cap commitment fact that commitment scheme is additively homomorphic 362 | let w_cap_commitment_calculated = super::super::utils::w_cap::<<TestCurve as Pairing>::G1>( 363 | domain.size(), 364 | f_commitment, 365 | q_commitment, 366 | rho, 367 | ); 368 | 369 | assert_eq!(w_cap_commitment_expected, w_cap_commitment_calculated); 370 | 371 | // check evaluations 372 | let w_cap_eval = w_cap_poly.evaluate(&rho); 373 | let g_eval = g_poly.evaluate(&rho); 374 | let g_omega_eval = g_poly.evaluate(&(rho * domain.group_gen())); 375 | let sum = super::super::utils::w1_w2_w3_evals_sum(&domain, g_eval, g_omega_eval, rho, t); 376 | assert_eq!(sum, w_cap_eval); 377 | } 378 | 379 | #[test] 380 | fn compute_w1_part_success() { 381 | let rng = &mut test_rng(); 382 | let n = 8usize; 383 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 384 | let z = Scalar::from(92u8); 385 | let alpha = Scalar::rand(rng); 386 | let beta = Scalar::rand(rng); 387 | let g_poly = super::g(&domain, z, alpha, beta); 388 | 389 | let rho = Scalar::rand(rng); 390 | let g_eval = g_poly.evaluate(&rho); 391 | 392 | let n_as_ref = Scalar::from(domain.size() as u8).into_bigint(); 393 | let one = Scalar::one(); 394 | let rho_n_minus_1 = rho.pow(n_as_ref) - one; 395 | 396 | let w1_part_poly = w1_part(&domain, &g_poly); 397 | 398 | assert_eq!( 399 | w1_part_poly.evaluate(&rho), 400 | g_eval * rho_n_minus_1 / (rho - one) 401 | ) 402 | } 403 | 404 | #[test] 405 | fn test_compute_w2_w3_part() { 406 | let rng = &mut test_rng(); 407 | 408 | let n = 8usize; 409 | let domain = GeneralEvaluationDomain::<Scalar>::new(n).unwrap(); 410 | let domain_2n = GeneralEvaluationDomain::<Scalar>::new(2 * n).unwrap(); 411 | 412 | let z = Scalar::from(92u8); 413 | let r = Scalar::rand(rng); 414 | let alpha = Scalar::rand(rng); 415 | let beta = Scalar::rand(rng); 416 | let f_poly = super::f(&domain, z, r); 417 | let g_poly = super::g(&domain, z, alpha, beta); 418 | let (_, w2) = super::w1_w2(&domain, &f_poly, &g_poly).unwrap(); 419 | let w3 = super::w3(&domain, &domain_2n, &g_poly).unwrap(); 420 | 421 | let tau = Scalar::rand(rng); 422 | let rho = Scalar::rand(rng); 423 | let g_eval = g_poly.evaluate(&rho); 424 | let g_omega_eval = g_poly.evaluate(&(rho * domain.group_gen())); 425 | 426 | let (_, rho_n_minus_1) = super::super::utils::rho_relations(domain.size(), rho); 427 | let one = Scalar::one(); 428 | let two = Scalar::from(2u8); 429 | let w_n_minus_1 = domain.elements().last().unwrap(); 430 | 431 | let (w2_part_poly, w3_part_poly) = w2_w3_parts(&w2, &w3, tau); 432 | 433 | assert_eq!( 434 | w2_part_poly.evaluate(&rho), 435 | tau * g_eval * (one - g_eval) * (rho_n_minus_1) / (rho - w_n_minus_1) 436 | ); 437 | 438 | assert_eq!(w3_part_poly.evaluate(&rho), { 439 | let part_a = g_eval - (two * g_omega_eval); 440 | let part_b = one - part_a; 441 | let part_c = rho - w_n_minus_1; 442 | tau * tau * part_a * part_b * part_c 443 | }); 444 | } 445 | } 446 | -------------------------------------------------------------------------------- /src/range_proof/utils.rs: -------------------------------------------------------------------------------- 1 | use ark_ec::CurveGroup; 2 | use ark_ff::PrimeField; 3 | use ark_poly::{EvaluationDomain, GeneralEvaluationDomain}; 4 | use ark_std::ops::{AddAssign, Mul}; 5 | use ark_std::Zero; 6 | 7 | // returns (rho^n - 1) / (rho - 1) and (rho^n - 1) 8 | pub fn rho_relations<S: PrimeField>(size: usize, rho: S) -> (S, S) { 9 | let n_as_ref = S::from(size as u8).into_bigint(); 10 | let one = S::one(); 11 | let rho_n_minus_1 = rho.pow(n_as_ref) - one; 12 | let rho_n_minus_1_by_rho_minus_1 = rho_n_minus_1 / (rho - one); 13 | 14 | (rho_n_minus_1_by_rho_minus_1, rho_n_minus_1) 15 | } 16 | 17 | // computes the sum of 18 | // - w1(x) = g * (x^n - 1) / (x - 1) // note that we don't compute (g - f) here 19 | // - w2(x) = g * (1 - g) * (x^n - 1) / (x - omega^{n - 1}) 20 | // - w3(x) = (g(x) - 2 * g(x * omega)) * (1 - g(x) + 2 * g(x * omega)) * (x - omega^{n - 1}) 21 | // 22 | // where g = g(rho), f = f(rho), i.e. the polynomial evaluations at point rho, n is the domain size 23 | // and omega denotes the roots of unity 24 | pub fn w1_w2_w3_evals_sum<S: PrimeField>( 25 | domain: &GeneralEvaluationDomain<S>, 26 | g_eval: S, 27 | g_omega_eval: S, 28 | rho: S, 29 | tau: S, 30 | ) -> S { 31 | let (rho_n_minus_1_by_rho_minus_1, rho_n_minus_1) = rho_relations(domain.size(), rho); 32 | let one = S::one(); 33 | let two = S::from(2u8); 34 | let w_n_minus_1 = domain.elements().last().unwrap(); 35 | // w1_part 36 | let w1_eval = g_eval * rho_n_minus_1_by_rho_minus_1; 37 | // w2 38 | let w2_eval = g_eval * (one - g_eval) * rho_n_minus_1 / (rho - w_n_minus_1); 39 | // w3 40 | let w3_eval = { 41 | let part_a = g_eval - (two * g_omega_eval); 42 | let part_b = one - part_a; 43 | let part_c = rho - w_n_minus_1; 44 | part_a * part_b * part_c 45 | }; 46 | 47 | w1_eval + tau * w2_eval + tau.square() * w3_eval 48 | } 49 | 50 | // returns w_cap(x) = f(x) * (rho^n - 1) / (rho - 1) + q(x) * (rho^n - 1) 51 | pub fn w_cap<C: CurveGroup>( 52 | size: usize, 53 | f_commitment: C::Affine, 54 | q_commitment: C::Affine, 55 | rho: C::ScalarField, 56 | ) -> C::Affine { 57 | let (rho_relation_1, rho_relation_2) = rho_relations(size, rho); 58 | let f_commit = f_commitment * rho_relation_1; 59 | let q_commit = q_commitment * rho_relation_2; 60 | (f_commit + q_commit).into() 61 | } 62 | 63 | pub fn aggregate<T, S>(values: &[T], by: S) -> T 64 | where 65 | S: PrimeField, 66 | T: Sized + Zero + Mul<S> + AddAssign<<T as Mul<S>>::Output> + Copy, 67 | { 68 | let mut acc = S::one(); 69 | let mut result = T::zero(); 70 | 71 | for &value in values { 72 | let tmp = value * acc; 73 | result += tmp; 74 | acc *= by; 75 | } 76 | 77 | result 78 | } 79 | -------------------------------------------------------------------------------- /src/tests/mod.rs: -------------------------------------------------------------------------------- 1 | pub use ark_bls12_381::{Bls12_381 as TestCurve, G1Affine}; 2 | use ark_ec::pairing::Pairing; 3 | use ark_ff::PrimeField; 4 | use ark_poly::univariate::DensePolynomial; 5 | use criterion as _; 6 | pub use sha3::Keccak256 as TestHash; 7 | 8 | pub const N: usize = Scalar::MODULUS_BIT_SIZE as usize / crate::encrypt::elgamal::MAX_BITS + 1; 9 | 10 | pub type Scalar = <TestCurve as Pairing>::ScalarField; 11 | pub type UniPoly = DensePolynomial<Scalar>; 12 | 13 | /* 14 | pub type Elgamal = crate::encrypt::elgamal::ExponentialElgamal<<BlsCurve as Pairing>::G1>; 15 | pub type ElgamalEncryptionProof = crate::veck::kzg_elgamal::EncryptionProof<{ N }, BlsCurve, Keccak256>; 16 | pub type KzgElgamalProof = crate::veck::kzg_elgamal::Proof<{ N }, BlsCurve, Keccak256>; 17 | pub type DleqProof = crate::dleq::Proof<<BlsCurve as Pairing>::G1, Keccak256>; 18 | pub type RangeProof = crate::range_proof::RangeProof<BlsCurve, Keccak256>; 19 | pub type PaillierEncryptionProof = crate::veck::kzg_paillier::Proof<BlsCurve, Keccak256>; 20 | */ 21 | -------------------------------------------------------------------------------- /src/veck/kzg/elgamal/encryption.rs: -------------------------------------------------------------------------------- 1 | use crate::commit::kzg::Powers; 2 | use crate::encrypt::elgamal::{Cipher, ExponentialElgamal as Elgamal, SplitScalar, MAX_BITS}; 3 | use crate::encrypt::EncryptionEngine; 4 | use crate::range_proof::RangeProof; 5 | use ark_ec::pairing::Pairing; 6 | use ark_ec::{AffineRepr, CurveGroup}; 7 | use ark_std::rand::Rng; 8 | use digest::Digest; 9 | #[cfg(feature = "parallel")] 10 | use rayon::prelude::*; 11 | 12 | /// A publicly verifiable proof based on the Elgamal encryption scheme. 13 | #[derive(Clone)] 14 | pub struct EncryptionProof<const N: usize, C: Pairing, D: Clone + Digest> { 15 | /// The actual Elgamal ciphertexts of the encrypted data points. 16 | pub ciphers: Vec<Cipher<C::G1>>, 17 | /// Each ciphertext is split into a set of scalars that, once decrypted, can reconstruct the 18 | /// original data point. Since we use the exponential Elgamal encryption scheme, these "short" 19 | /// ciphertexts are needed to encrypt split data points in the bruteforceable range: 2^32. 20 | pub short_ciphers: Vec<[Cipher<C::G1>; N]>, 21 | /// Each "short" ciphertext requires a range proof proving that the encrypted value is in the 22 | /// bruteforceable range. 23 | pub range_proofs: Vec<[RangeProof<C, D>; N]>, 24 | /// Random encryption points used to encrypt the original data points. These are the `h^r` 25 | /// values in the exponential Elgamal scheme: `e = g^m * h^r`, where `e` is the ciphertext, `m` 26 | /// is the plaintext. 27 | pub random_encryption_points: Vec<C::G1Affine>, 28 | } 29 | 30 | impl<const N: usize, C: Pairing, D: Clone + Digest> Default for EncryptionProof<N, C, D> { 31 | fn default() -> Self { 32 | Self { 33 | ciphers: Vec::new(), 34 | short_ciphers: Vec::new(), 35 | range_proofs: Vec::new(), 36 | random_encryption_points: Vec::new(), 37 | } 38 | } 39 | } 40 | 41 | impl<const N: usize, C: Pairing, D: Clone + Digest + Send + Sync> EncryptionProof<N, C, D> { 42 | pub fn new<R: Rng + Send + Sync>( 43 | evaluations: &[C::ScalarField], 44 | encryption_pk: &<Elgamal<C::G1> as EncryptionEngine>::EncryptionKey, 45 | powers: &Powers<C>, 46 | _rng: &mut R, 47 | ) -> Self { 48 | #[cfg(not(feature = "parallel"))] 49 | let proof = evaluations.iter().fold(Self::default(), |acc, eval| { 50 | acc.append(eval, encryption_pk, powers, _rng) 51 | }); 52 | 53 | #[cfg(feature = "parallel")] 54 | let proof = evaluations 55 | .par_iter() 56 | .fold(Self::default, |acc, eval| { 57 | let rng = &mut ark_std::rand::thread_rng(); 58 | acc.append(eval, encryption_pk, powers, rng) 59 | }) 60 | .reduce(Self::default, |acc, proof| acc.extend(proof)); 61 | proof 62 | } 63 | 64 | fn append<R: Rng>( 65 | mut self, 66 | eval: &C::ScalarField, 67 | encryption_pk: &<Elgamal<C::G1> as EncryptionEngine>::EncryptionKey, 68 | powers: &Powers<C>, 69 | rng: &mut R, 70 | ) -> Self { 71 | let split_eval = SplitScalar::from(*eval); 72 | let rp = split_eval 73 | .splits() 74 | .map(|s| RangeProof::new(s, MAX_BITS, powers, rng).expect("invalid range proof input")); 75 | let (sc, rand) = split_eval.encrypt::<Elgamal<C::G1>, _>(encryption_pk, rng); 76 | let cipher = <Elgamal<C::G1> as EncryptionEngine>::encrypt_with_randomness( 77 | eval, 78 | encryption_pk, 79 | &rand, 80 | ); 81 | self.random_encryption_points 82 | .push((C::G1Affine::generator() * rand).into_affine()); 83 | self.ciphers.push(cipher); 84 | self.short_ciphers.push(sc); 85 | self.range_proofs.push(rp); 86 | self 87 | } 88 | 89 | fn extend(mut self, other: Self) -> Self { 90 | self.random_encryption_points 91 | .extend(other.random_encryption_points); 92 | self.ciphers.extend(other.ciphers); 93 | self.short_ciphers.extend(other.short_ciphers); 94 | self.range_proofs.extend(other.range_proofs); 95 | self 96 | } 97 | 98 | /// Generates a subset from the total encrypted data. 99 | /// 100 | /// Clients might not be interested in the whole dataset, thus the server may generate a subset 101 | /// encryption proof to reduce proof verification costs. 102 | pub fn subset(&self, indices: &[usize]) -> Self { 103 | let size = indices.len(); 104 | let mut ciphers = Vec::with_capacity(size); 105 | let mut short_ciphers = Vec::with_capacity(size); 106 | let mut random_encryption_points = Vec::with_capacity(size); 107 | let mut range_proofs = Vec::with_capacity(size); 108 | for &index in indices { 109 | ciphers.push(self.ciphers[index]); 110 | short_ciphers.push(self.short_ciphers[index]); 111 | random_encryption_points.push(self.random_encryption_points[index]); 112 | range_proofs.push(self.range_proofs[index].clone()); 113 | } 114 | 115 | Self { 116 | ciphers, 117 | short_ciphers, 118 | range_proofs, 119 | random_encryption_points, 120 | } 121 | } 122 | 123 | /// Checks that the sum of split scalars evaluate to the encrypted value via the homomorphic 124 | /// properties of Elgamal encryption. 125 | pub fn verify_split_scalars(&self) -> bool { 126 | #[cfg(feature = "parallel")] 127 | let result = self 128 | .ciphers 129 | .par_iter() 130 | .zip(&self.short_ciphers) 131 | .fold( 132 | || true, 133 | |acc, (cipher, short_cipher)| acc && cipher.check_encrypted_sum(short_cipher), 134 | ) 135 | .reduce(|| true, |acc: bool, sub_boolean: bool| acc && sub_boolean); 136 | 137 | #[cfg(not(feature = "parallel"))] 138 | let result = self 139 | .ciphers 140 | .iter() 141 | .zip(&self.short_ciphers) 142 | .fold(true, |acc, (cipher, short_cipher)| { 143 | acc && cipher.check_encrypted_sum(short_cipher) 144 | }); 145 | result 146 | } 147 | 148 | // TODO range proofs and short ciphers are not "connected" by anything? 149 | // https://github.com/PopcornPaws/fde/issues/13 150 | pub fn verify_range_proofs(&self, powers: &Powers<C>) -> bool { 151 | #[cfg(feature = "parallel")] 152 | let result = self 153 | .range_proofs 154 | .par_iter() 155 | .fold( 156 | || true, 157 | |acc, rps| acc && rps.par_iter().all(|rp| rp.verify(MAX_BITS, powers).is_ok()), 158 | ) 159 | .reduce(|| true, |acc: bool, sub_boolean: bool| acc && sub_boolean); 160 | 161 | #[cfg(not(feature = "parallel"))] 162 | let result = self.range_proofs.iter().fold(true, |acc, rps| { 163 | acc && rps.par_iter.all(|rp| rp.verify(MAX_BITS, powers)).is_ok() 164 | }); 165 | result 166 | } 167 | } 168 | 169 | #[cfg(test)] 170 | mod test { 171 | use super::*; 172 | use crate::tests::*; 173 | use ark_ec::Group; 174 | use ark_std::{test_rng, UniformRand}; 175 | 176 | const DATA_SIZE: usize = 16; 177 | 178 | type ElgamalEncryptionProof = EncryptionProof<{ N }, TestCurve, TestHash>; 179 | 180 | #[test] 181 | fn encryption_proof() { 182 | let rng = &mut test_rng(); 183 | let tau = Scalar::rand(rng); // "secret" tau 184 | let powers = Powers::<TestCurve>::unsafe_setup(tau, (DATA_SIZE + 1).max(MAX_BITS * 4)); // generate powers of tau size DATA_SIZE 185 | 186 | let encryption_sk = Scalar::rand(rng); 187 | let encryption_pk = (<TestCurve as Pairing>::G1::generator() * encryption_sk).into_affine(); 188 | 189 | let data: Vec<Scalar> = (0..DATA_SIZE).map(|_| Scalar::rand(rng)).collect(); 190 | let mut encryption_proof = ElgamalEncryptionProof::new(&data, &encryption_pk, &powers, rng); 191 | 192 | assert!(encryption_proof.verify_split_scalars()); 193 | assert!(encryption_proof.verify_range_proofs(&powers)); 194 | 195 | // manually modify the encryption proof so that it fails 196 | encryption_proof.short_ciphers[DATA_SIZE - 3][2] = Default::default(); 197 | assert!(!encryption_proof.verify_split_scalars()); 198 | 199 | encryption_proof.range_proofs[DATA_SIZE - 3][3] = 200 | RangeProof::new(Scalar::from(123u8), 10, &powers, rng).unwrap(); 201 | assert!(!encryption_proof.verify_range_proofs(&powers)); 202 | } 203 | } 204 | -------------------------------------------------------------------------------- /src/veck/kzg/elgamal/mod.rs: -------------------------------------------------------------------------------- 1 | mod encryption; 2 | pub use encryption::EncryptionProof; 3 | 4 | use crate::commit::kzg::{Kzg, Powers}; 5 | use crate::dleq::Proof as DleqProof; 6 | use crate::hash::Hasher; 7 | use crate::Error as CrateError; 8 | use ark_ec::pairing::Pairing; 9 | use ark_ec::{AffineRepr, CurveGroup, VariableBaseMSM as Msm}; 10 | use ark_ff::PrimeField; 11 | use ark_poly::domain::general::GeneralEvaluationDomain; 12 | use ark_poly::univariate::DensePolynomial; 13 | use ark_poly::EvaluationDomain; 14 | use ark_poly::Polynomial; 15 | use ark_std::marker::PhantomData; 16 | use ark_std::rand::Rng; 17 | use digest::Digest; 18 | 19 | use thiserror::Error as ErrorT; 20 | 21 | #[derive(Debug, ErrorT, PartialEq)] 22 | pub enum Error { 23 | #[error("invalid DLEQ proof for split encryption points")] 24 | InvalidDleqProof, 25 | #[error("invalid KZG proof")] 26 | InvalidKzgProof, 27 | #[error("invalid subset polynomial proof")] 28 | InvalidSubsetPolynomial, 29 | #[error("invalid split scalar verification")] 30 | InvalidSplitScalars, 31 | #[error("invalid range proofs")] 32 | InvalidRangeProofs, 33 | } 34 | 35 | pub struct Proof<const N: usize, C: Pairing, D: Clone + Digest> { 36 | pub encryption_proof: EncryptionProof<N, C, D>, 37 | pub challenge_eval_commitment: C::G1Affine, 38 | pub challenge_opening_proof: C::G1Affine, 39 | pub dleq_proof: DleqProof<C::G1, D>, 40 | pub com_f_q_poly: C::G1Affine, 41 | _poly: PhantomData<DensePolynomial<C::ScalarField>>, 42 | _digest: PhantomData<D>, 43 | } 44 | 45 | impl<const N: usize, C, D> Proof<N, C, D> 46 | where 47 | C: Pairing, 48 | D: Digest + Clone + Send + Sync, 49 | { 50 | pub fn new<R: Rng>( 51 | f_poly: &DensePolynomial<C::ScalarField>, 52 | f_s_poly: &DensePolynomial<C::ScalarField>, 53 | encryption_sk: &C::ScalarField, 54 | encryption_proof: EncryptionProof<N, C, D>, 55 | powers: &Powers<C>, 56 | rng: &mut R, 57 | ) -> Result<Self, CrateError> { 58 | let mut hasher = Hasher::<D>::new(); 59 | encryption_proof 60 | .ciphers 61 | .iter() 62 | .for_each(|cipher| hasher.update(&cipher.c1())); 63 | 64 | let domain_size = encryption_proof.ciphers.len(); 65 | let domain = GeneralEvaluationDomain::<C::ScalarField>::new(domain_size) 66 | .ok_or(CrateError::InvalidFftDomain(domain_size))?; 67 | 68 | // challenge and KZG proof 69 | let challenge = C::ScalarField::from_le_bytes_mod_order(&hasher.finalize()); 70 | let challenge_eval = f_s_poly.evaluate(&challenge); 71 | let challenge_opening_proof = Kzg::proof(f_s_poly, challenge, challenge_eval, powers); 72 | let challenge_eval_commitment = (C::G1Affine::generator() * challenge_eval).into_affine(); 73 | 74 | // NOTE According to the docs this should always return Some((q, rem)), so unwrap is fine 75 | // https://docs.rs/ark-poly/latest/src/ark_poly/polynomial/univariate/dense.rs.html#144 76 | let f_q_poly = (f_poly - f_s_poly) 77 | .divide_by_vanishing_poly(domain) 78 | .unwrap() 79 | .0; 80 | // subset polynomial KZG commitment 81 | let com_f_q_poly = powers.commit_g1(&f_q_poly).into(); 82 | 83 | // DLEQ proof 84 | let lagrange_evaluations = &domain.evaluate_all_lagrange_coefficients(challenge); 85 | let q_point: C::G1 = Msm::msm_unchecked( 86 | &encryption_proof.random_encryption_points, 87 | lagrange_evaluations, 88 | ); 89 | 90 | let dleq_proof = DleqProof::new( 91 | encryption_sk, 92 | q_point.into_affine(), 93 | C::G1Affine::generator(), 94 | rng, 95 | ); 96 | 97 | Ok(Self { 98 | encryption_proof, 99 | challenge_eval_commitment, 100 | challenge_opening_proof, 101 | dleq_proof, 102 | com_f_q_poly, 103 | _poly: PhantomData, 104 | _digest: PhantomData, 105 | }) 106 | } 107 | 108 | pub fn verify( 109 | &self, 110 | com_f_poly: C::G1, 111 | com_f_s_poly: C::G1, 112 | encryption_pk: C::G1Affine, 113 | powers: &Powers<C>, 114 | ) -> Result<(), CrateError> { 115 | let mut hasher = Hasher::<D>::new(); 116 | let c1_points: Vec<C::G1Affine> = self 117 | .encryption_proof 118 | .ciphers 119 | .iter() 120 | .map(|cipher| { 121 | let c1 = cipher.c1(); 122 | hasher.update(&c1); 123 | c1 124 | }) 125 | .collect(); 126 | let challenge = C::ScalarField::from_le_bytes_mod_order(&hasher.finalize()); 127 | let domain_size = self.encryption_proof.ciphers.len(); 128 | let domain = GeneralEvaluationDomain::<C::ScalarField>::new(domain_size) 129 | .ok_or(CrateError::InvalidFftDomain(domain_size))?; 130 | 131 | // polynomial division check via vanishing polynomial 132 | let vanishing_poly = DensePolynomial::from(domain.vanishing_polynomial()); 133 | let com_vanishing_poly = powers.commit_g2(&vanishing_poly); 134 | let subset_pairing_check = Kzg::<C>::pairing_check( 135 | com_f_poly - com_f_s_poly, 136 | self.com_f_q_poly.into_group(), 137 | com_vanishing_poly, 138 | ); 139 | 140 | // DLEQ check 141 | let lagrange_evaluations = &domain.evaluate_all_lagrange_coefficients(challenge); 142 | let q_point: C::G1 = Msm::msm_unchecked( 143 | &self.encryption_proof.random_encryption_points, 144 | lagrange_evaluations, 145 | ); // Q 146 | let ct_point: C::G1 = Msm::msm_unchecked(&c1_points, lagrange_evaluations); // C_t 147 | 148 | let q_star = ct_point - self.challenge_eval_commitment; // Q* = C_t / C_alpha 149 | let dleq_check = self.dleq_proof.verify( 150 | q_point.into(), 151 | q_star, 152 | C::G1Affine::generator(), 153 | encryption_pk.into(), 154 | ); 155 | 156 | // KZG pairing check 157 | let point = C::G2Affine::generator() * challenge; 158 | let kzg_check = Kzg::verify( 159 | self.challenge_opening_proof, 160 | com_f_s_poly.into(), 161 | point, 162 | self.challenge_eval_commitment.into_group(), 163 | powers, 164 | ); 165 | 166 | // check that split scalars are in a brute-forceable range 167 | 168 | if !dleq_check { 169 | Err(Error::InvalidDleqProof.into()) 170 | } else if !kzg_check { 171 | Err(Error::InvalidKzgProof.into()) 172 | } else if !subset_pairing_check { 173 | Err(Error::InvalidSubsetPolynomial.into()) 174 | } else if !self.encryption_proof.verify_split_scalars() { 175 | Err(Error::InvalidSplitScalars.into()) 176 | } else if !self.encryption_proof.verify_range_proofs(powers) { 177 | Err(Error::InvalidRangeProofs.into()) 178 | } else { 179 | Ok(()) 180 | } 181 | } 182 | } 183 | 184 | #[cfg(test)] 185 | mod test { 186 | use super::*; 187 | use crate::encrypt::elgamal::MAX_BITS; 188 | use crate::tests::*; 189 | use ark_ec::Group; 190 | use ark_poly::Evaluations; 191 | use ark_std::{test_rng, UniformRand}; 192 | 193 | const DATA_SIZE: usize = 16; 194 | const SUBSET_SIZE: usize = 8; 195 | 196 | type ElgamalEncryptionProof = EncryptionProof<{ N }, TestCurve, TestHash>; 197 | type KzgElgamalProof = Proof<{ N }, TestCurve, TestHash>; 198 | 199 | #[test] 200 | fn flow() { 201 | // KZG setup simulation 202 | let rng = &mut test_rng(); 203 | let tau = Scalar::rand(rng); // "secret" tau 204 | let powers = Powers::<TestCurve>::unsafe_setup(tau, (DATA_SIZE + 1).max(MAX_BITS * 4)); // generate powers of tau size DATA_SIZE 205 | 206 | // Server's (elphemeral?) encryption key for this session 207 | let encryption_sk = Scalar::rand(rng); 208 | let encryption_pk = (<TestCurve as Pairing>::G1::generator() * encryption_sk).into_affine(); 209 | 210 | // Generate random data and public inputs (encrypted data, etc) 211 | let data: Vec<Scalar> = (0..DATA_SIZE).map(|_| Scalar::rand(rng)).collect(); 212 | let encryption_proof = ElgamalEncryptionProof::new(&data, &encryption_pk, &powers, rng); 213 | 214 | assert!(encryption_proof.verify_range_proofs(&powers)); 215 | 216 | let domain = GeneralEvaluationDomain::new(data.len()).expect("valid domain"); 217 | let index_map = crate::veck::index_map(domain); 218 | 219 | // Interpolate original polynomial and compute its KZG commitment. 220 | // This is performed only once by the server 221 | let evaluations = Evaluations::from_vec_and_domain(data, domain); 222 | let f_poly: UniPoly = evaluations.interpolate_by_ref(); 223 | let com_f_poly = powers.commit_g1(&f_poly); 224 | 225 | // get subdomain with size suitable for interpolating a polynomial with SUBSET_SIZE 226 | // coefficients 227 | let subdomain = GeneralEvaluationDomain::new(SUBSET_SIZE).unwrap(); 228 | let subset_indices = crate::veck::subset_indices(&index_map, &subdomain); 229 | let subset_evaluations = 230 | crate::veck::subset_evals(&evaluations, &subset_indices, subdomain); 231 | let f_s_poly: UniPoly = subset_evaluations.interpolate_by_ref(); 232 | let com_f_s_poly = powers.commit_g1(&f_s_poly); 233 | 234 | let sub_encryption_proof = encryption_proof.subset(&subset_indices); 235 | 236 | let proof = KzgElgamalProof::new( 237 | &f_poly, 238 | &f_s_poly, 239 | &encryption_sk, 240 | sub_encryption_proof, 241 | &powers, 242 | rng, 243 | ) 244 | .unwrap(); 245 | assert!(proof 246 | .verify(com_f_poly, com_f_s_poly, encryption_pk, &powers) 247 | .is_ok()); 248 | } 249 | } 250 | -------------------------------------------------------------------------------- /src/veck/kzg/mod.rs: -------------------------------------------------------------------------------- 1 | pub mod elgamal; 2 | pub mod paillier; 3 | -------------------------------------------------------------------------------- /src/veck/kzg/paillier/encrypt.rs: -------------------------------------------------------------------------------- 1 | use super::utils::pow_mult_mod; 2 | use ark_std::One; 3 | use num_bigint::BigUint; 4 | #[cfg(feature = "parallel")] 5 | use rayon::prelude::*; 6 | 7 | pub fn encrypt(value: &BigUint, key: &BigUint, random: &BigUint) -> BigUint { 8 | let n2 = key * key; 9 | pow_mult_mod(&(key + BigUint::one()), value, random, key, &n2) 10 | } 11 | 12 | #[cfg(not(feature = "parallel"))] 13 | pub fn batch<T: AsRef<[BigUint]>>(values: T, key: &BigUint, randoms: T) -> Vec<BigUint> { 14 | values 15 | .as_ref() 16 | .iter() 17 | .zip(randoms.as_ref()) 18 | .map(|(val, rand)| encrypt(val, key, rand)) 19 | .collect() 20 | } 21 | 22 | #[cfg(feature = "parallel")] 23 | pub fn batch<T>(values: T, key: &BigUint, randoms: T) -> Vec<BigUint> 24 | where 25 | T: AsRef<[BigUint]> + rayon::iter::IntoParallelIterator, 26 | { 27 | values 28 | .as_ref() 29 | .par_iter() 30 | .zip(randoms.as_ref()) 31 | .map(|(val, rand)| encrypt(val, key, rand)) 32 | .collect() 33 | } 34 | -------------------------------------------------------------------------------- /src/veck/kzg/paillier/mod.rs: -------------------------------------------------------------------------------- 1 | mod encrypt; 2 | mod random; 3 | mod server; 4 | mod utils; 5 | pub use random::RandomParameters; 6 | pub use server::Server; 7 | use utils::{challenge, modular_inverse, pow_mult_mod}; 8 | 9 | use crate::commit::kzg::Powers; 10 | use crate::Error as CrateError; 11 | use ark_ec::pairing::Pairing; 12 | use ark_ec::Group; 13 | use ark_ff::fields::PrimeField; 14 | use ark_poly::univariate::DensePolynomial; 15 | use ark_poly::{EvaluationDomain, GeneralEvaluationDomain}; 16 | use ark_std::marker::PhantomData; 17 | use ark_std::rand::Rng; 18 | use ark_std::One; 19 | use digest::Digest; 20 | use num_bigint::BigUint; 21 | 22 | use thiserror::Error as ErrorT; 23 | 24 | const N_BITS: u64 = 1024; 25 | 26 | #[derive(ErrorT, Debug, PartialEq)] 27 | pub enum Error { 28 | #[error("invalid encrypted value, has no modular inverse")] 29 | InvalidEncryptedValue, 30 | #[error("computed challenge does not match the expected one")] 31 | ChallengeMismatch, 32 | #[error("pairing check failed for subset polynomial")] 33 | PairingMismatch, 34 | } 35 | 36 | pub struct Proof<C: Pairing, D> { 37 | pub challenge: BigUint, 38 | pub ct_vec: Vec<BigUint>, 39 | pub w_vec: Vec<BigUint>, 40 | pub z_vec: Vec<BigUint>, 41 | pub com_q_poly: C::G1, 42 | _digest: PhantomData<D>, 43 | _curve: PhantomData<C>, 44 | } 45 | 46 | impl<C: Pairing, D: Digest> Proof<C, D> { 47 | #[allow(clippy::too_many_arguments)] 48 | pub fn new<R: Rng>( 49 | values: &[BigUint], 50 | f_poly: &DensePolynomial<C::ScalarField>, 51 | f_s_poly: &DensePolynomial<C::ScalarField>, 52 | com_f_poly: &C::G1, 53 | com_f_s_poly: &C::G1, 54 | domain: &GeneralEvaluationDomain<C::ScalarField>, 55 | domain_s: &GeneralEvaluationDomain<C::ScalarField>, 56 | pubkey: &BigUint, 57 | powers: &Powers<C>, 58 | rng: &mut R, 59 | ) -> Self { 60 | let vanishing_poly = DensePolynomial::from(domain_s.vanishing_polynomial()); 61 | let q_poly = &(f_poly - f_s_poly) / &vanishing_poly; 62 | let q_poly_evals = q_poly.evaluate_over_domain_by_ref(*domain); 63 | let com_q_poly = powers.commit_scalars_g1(&q_poly_evals.evals); 64 | 65 | let random_params = RandomParameters::new(values.len(), rng); 66 | let ct_vec = encrypt::batch(values, pubkey, &random_params.u_vec); 67 | let t_vec = encrypt::batch(&random_params.r_vec, pubkey, &random_params.s_vec); 68 | let r_scalar_vec: Vec<C::ScalarField> = random_params 69 | .r_vec 70 | .iter() 71 | .map(|r| C::ScalarField::from_le_bytes_mod_order(&r.to_bytes_le())) 72 | .collect(); 73 | let t = powers.commit_scalars_g1(&r_scalar_vec); 74 | let challenge = challenge::<C::G1, D>( 75 | pubkey, 76 | &vanishing_poly, 77 | &ct_vec, 78 | com_f_poly, 79 | com_f_s_poly, 80 | &t_vec, 81 | &t, 82 | ); 83 | let w_vec: Vec<BigUint> = random_params 84 | .s_vec 85 | .iter() 86 | .zip(&random_params.u_vec) 87 | .map(|(s, u)| pow_mult_mod(s, &BigUint::one(), u, &challenge, pubkey)) 88 | .collect(); 89 | let z_vec: Vec<BigUint> = random_params 90 | .r_vec 91 | .iter() 92 | .zip(values) 93 | .map(|(r, val)| r + &challenge * val) 94 | .collect(); 95 | 96 | Self { 97 | challenge, 98 | ct_vec, 99 | w_vec, 100 | z_vec, 101 | com_q_poly, 102 | _digest: PhantomData, 103 | _curve: PhantomData, 104 | } 105 | } 106 | 107 | pub fn verify( 108 | &self, 109 | com_f_poly: &C::G1, 110 | com_f_s_poly: &C::G1, 111 | domain: &GeneralEvaluationDomain<C::ScalarField>, 112 | domain_s: &GeneralEvaluationDomain<C::ScalarField>, 113 | pubkey: &BigUint, 114 | powers: &Powers<C>, 115 | ) -> Result<(), CrateError> { 116 | let vanishing_poly = DensePolynomial::from(domain_s.vanishing_polynomial()); 117 | let vanishing_poly_evals = vanishing_poly.evaluate_over_domain_by_ref(*domain); 118 | let com_vanishing_poly_g2 = powers.commit_scalars_g2(&vanishing_poly_evals.evals); 119 | 120 | let lhs_pairing = C::pairing(self.com_q_poly, com_vanishing_poly_g2); 121 | let rhs_pairing = C::pairing(*com_f_poly - com_f_s_poly, C::G2::generator()); 122 | if lhs_pairing != rhs_pairing { 123 | return Err(Error::PairingMismatch.into()); 124 | } 125 | 126 | let modulo = pubkey * pubkey; 127 | let t_vec_expected: Vec<BigUint> = self 128 | .ct_vec 129 | .iter() 130 | .zip(self.w_vec.iter().zip(&self.z_vec)) 131 | .flat_map(|(ct, (w, z))| -> Result<BigUint, CrateError> { 132 | let aux = pow_mult_mod(&(pubkey + BigUint::one()), z, w, pubkey, &modulo); 133 | let ct_pow_c = ct.modpow(&self.challenge, &modulo); 134 | let ct_pow_minus_c = 135 | modular_inverse(&ct_pow_c, &modulo).ok_or(Error::InvalidEncryptedValue)?; 136 | Ok((aux * ct_pow_minus_c) % &modulo) 137 | }) 138 | .collect::<Vec<_>>(); 139 | let z_scalar_vec: Vec<C::ScalarField> = self 140 | .z_vec 141 | .iter() 142 | .map(|z| C::ScalarField::from_le_bytes_mod_order(&z.to_bytes_le())) 143 | .collect(); 144 | 145 | // compute t 146 | let challenge_scalar = 147 | C::ScalarField::from_le_bytes_mod_order(&self.challenge.to_bytes_le()); 148 | let commitment_pow_challenge = *com_f_s_poly * challenge_scalar; 149 | let msm = powers.commit_scalars_g1(&z_scalar_vec); 150 | let t_expected = msm - commitment_pow_challenge; 151 | 152 | let challenge_expected = challenge::<C::G1, D>( 153 | pubkey, 154 | &vanishing_poly, 155 | &self.ct_vec, 156 | com_f_poly, 157 | com_f_s_poly, 158 | &t_vec_expected, 159 | &t_expected, 160 | ); 161 | 162 | if self.challenge != challenge_expected { 163 | Err(Error::ChallengeMismatch.into()) 164 | } else { 165 | Ok(()) 166 | } 167 | } 168 | 169 | pub fn decrypt(&self, server: &Server) -> Vec<BigUint> { 170 | let denominator = server.decryption_denominator(); 171 | let denominator_inv = modular_inverse(&denominator, &server.pubkey).unwrap(); 172 | self.ct_vec 173 | .iter() 174 | .map(|ct| { 175 | let ct_lx = server.lx(&ct.modpow(&server.privkey, &server.mod_n2)); 176 | (ct_lx * &denominator_inv) % &server.pubkey 177 | }) 178 | .collect() 179 | } 180 | } 181 | 182 | #[cfg(test)] 183 | mod test { 184 | use super::*; 185 | use crate::tests::*; 186 | use ark_ff::BigInteger; 187 | use ark_poly::Evaluations; 188 | use ark_std::{test_rng, UniformRand}; 189 | 190 | const DATA_SIZE: usize = 16; 191 | const SUBSET_SIZE: usize = 16; 192 | 193 | type PaillierEncryptionProof = Proof<TestCurve, TestHash>; 194 | 195 | #[test] 196 | fn flow() { 197 | // KZG setup simulation 198 | let rng = &mut test_rng(); 199 | // "secret" tau 200 | let tau = Scalar::rand(rng); 201 | // generate powers of tau size DATA_SIZE 202 | let powers = Powers::<TestCurve>::unsafe_setup_eip_4844(tau, DATA_SIZE); 203 | // new server (with encryption pubkey) 204 | let server = Server::new(rng); 205 | // random data to encrypt 206 | let data: Vec<Scalar> = (0..DATA_SIZE).map(|_| Scalar::rand(rng)).collect(); 207 | let domain = GeneralEvaluationDomain::new(DATA_SIZE).unwrap(); 208 | let domain_s = GeneralEvaluationDomain::new(SUBSET_SIZE).unwrap(); 209 | let evaluations = Evaluations::from_vec_and_domain(data, domain); 210 | let index_map = crate::veck::index_map(domain); 211 | let subset_indices = crate::veck::subset_indices(&index_map, &domain_s); 212 | let evaluations_s = crate::veck::subset_evals(&evaluations, &subset_indices, domain_s); 213 | 214 | let f_poly: UniPoly = evaluations.interpolate_by_ref(); 215 | let f_s_poly: UniPoly = evaluations_s.interpolate_by_ref(); 216 | 217 | let evaluations_s_d = f_s_poly.evaluate_over_domain_by_ref(domain); 218 | 219 | let com_f_poly = powers.commit_scalars_g1(&evaluations.evals); 220 | let com_f_s_poly = powers.commit_scalars_g1(&evaluations_s_d.evals); 221 | 222 | let data_biguint: Vec<BigUint> = evaluations_s 223 | .evals 224 | .iter() 225 | .map(|d| BigUint::from_bytes_le(&d.into_bigint().to_bytes_le())) 226 | .collect(); 227 | 228 | let proof = PaillierEncryptionProof::new( 229 | &data_biguint, 230 | &f_poly, 231 | &f_s_poly, 232 | &com_f_poly, 233 | &com_f_s_poly, 234 | &domain, 235 | &domain_s, 236 | &server.pubkey, 237 | &powers, 238 | rng, 239 | ); 240 | 241 | assert!(proof 242 | .verify( 243 | &com_f_poly, 244 | &com_f_s_poly, 245 | &domain, 246 | &domain_s, 247 | &server.pubkey, 248 | &powers 249 | ) 250 | .is_ok()); 251 | 252 | let decrypted_data = proof.decrypt(&server); 253 | assert_eq!(decrypted_data, data_biguint); 254 | } 255 | } 256 | -------------------------------------------------------------------------------- /src/veck/kzg/paillier/random.rs: -------------------------------------------------------------------------------- 1 | use super::N_BITS; 2 | use ark_std::rand::distributions::Distribution; 3 | use ark_std::rand::Rng; 4 | use num_bigint::{BigUint, RandomBits}; 5 | 6 | pub struct RandomParameters { 7 | pub u_vec: Vec<BigUint>, 8 | pub s_vec: Vec<BigUint>, 9 | pub r_vec: Vec<BigUint>, 10 | } 11 | 12 | impl RandomParameters { 13 | pub fn new<R: Rng>(size: usize, rng: &mut R) -> Self { 14 | let mut u_vec = Vec::with_capacity(size); 15 | let mut s_vec = Vec::with_capacity(size); 16 | let mut r_vec = Vec::with_capacity(size); 17 | let random_bits = RandomBits::new(N_BITS); 18 | let random_bits_2 = RandomBits::new(N_BITS >> 1); 19 | for _ in 0..size { 20 | u_vec.push(random_bits.sample(rng)); 21 | s_vec.push(random_bits.sample(rng)); 22 | r_vec.push(random_bits_2.sample(rng)); 23 | } 24 | 25 | Self { 26 | u_vec, 27 | s_vec, 28 | r_vec, 29 | } 30 | } 31 | } 32 | -------------------------------------------------------------------------------- /src/veck/kzg/paillier/server.rs: -------------------------------------------------------------------------------- 1 | use super::N_BITS; 2 | use ark_std::rand::distributions::Distribution; 3 | use ark_std::rand::Rng; 4 | use ark_std::One; 5 | use num_bigint::{BigUint, RandomBits}; 6 | use num_integer::Integer; 7 | use num_prime::nt_funcs::prev_prime; 8 | 9 | /// A simulated server instance tailored for the Paillier encryption scheme. 10 | #[derive(Debug)] 11 | pub struct Server { 12 | pub p_prime: BigUint, 13 | pub q_prime: BigUint, 14 | pub privkey: BigUint, 15 | pub pubkey: BigUint, 16 | pub mod_n2: BigUint, 17 | } 18 | 19 | impl Server { 20 | pub fn new<R: Rng>(rng: &mut R) -> Self { 21 | // generate small enough primes so that their product fits 22 | // "N_BITS" number of bits 23 | let (p, q) = primes(N_BITS >> 1, rng); 24 | let pubkey = &p * &q; 25 | let privkey = (&p - BigUint::one()).lcm(&(&q - BigUint::one())); 26 | let mod_n2 = &pubkey * &pubkey; 27 | 28 | Self { 29 | p_prime: p, 30 | q_prime: q, 31 | privkey, 32 | pubkey, 33 | mod_n2, 34 | } 35 | } 36 | 37 | /// Helper function to compute L(x) = (x - 1) / N 38 | pub fn lx(&self, x: &BigUint) -> BigUint { 39 | debug_assert!(x < &self.mod_n2 && (x % &self.pubkey) == BigUint::one()); 40 | (x - BigUint::one()) / &self.pubkey 41 | } 42 | 43 | /// Helper function to compute the denominator in the Paillier decryption scheme equation. 44 | /// 45 | /// x = (N + 1)^{sk} mod N^2 46 | /// L(x) = (x - 1) / N 47 | pub fn decryption_denominator(&self) -> BigUint { 48 | let n_plus_1_pow_sk = (&self.pubkey + BigUint::one()).modpow(&self.privkey, &self.mod_n2); 49 | self.lx(&n_plus_1_pow_sk) 50 | } 51 | } 52 | 53 | fn primes<R: Rng>(n_bits: u64, rng: &mut R) -> (BigUint, BigUint) { 54 | let random_bits = RandomBits::new(n_bits); 55 | let target_p: BigUint = random_bits.sample(rng); 56 | let target_q: BigUint = random_bits.sample(rng); 57 | let p = find_next_smaller_prime(&target_p); 58 | let q = find_next_smaller_prime(&target_q); 59 | debug_assert_ne!(p, q); 60 | (p, q) 61 | } 62 | 63 | fn find_next_smaller_prime(target: &BigUint) -> BigUint { 64 | // look for previous prime because we need to fit into 2 * n bits when we multiply p and q 65 | loop { 66 | if let Some(found) = prev_prime(target, None) { 67 | return found; 68 | } 69 | } 70 | } 71 | -------------------------------------------------------------------------------- /src/veck/kzg/paillier/utils.rs: -------------------------------------------------------------------------------- 1 | use crate::hash::Hasher; 2 | use ark_ec::CurveGroup; 3 | use ark_poly::univariate::DensePolynomial; 4 | use ark_std::One; 5 | use digest::Digest; 6 | use num_bigint::{BigInt, BigUint, Sign}; 7 | use num_integer::Integer; 8 | 9 | /// Computes `(a^alpha mod N) * (b^beta mod N) mod N`. 10 | pub fn pow_mult_mod( 11 | a: &BigUint, 12 | alpha: &BigUint, 13 | b: &BigUint, 14 | beta: &BigUint, 15 | modulo: &BigUint, 16 | ) -> BigUint { 17 | (a.modpow(alpha, modulo) * b.modpow(beta, modulo)) % modulo 18 | } 19 | 20 | /// Modular inverse helper for `BigUint` types. Returns `None` if the inverse does not exist. 21 | /// 22 | /// `BigUint`'s`modpow` cannot handle negative exponents, it panics. Thus, we are using the 23 | /// extended GCD algorithm to find the modular inverse of `num`. However, `extended_gcd_lcm` is 24 | /// only implemented for signed types such as `BigInt`, hence the conversions. 25 | pub fn modular_inverse(num: &BigUint, modulo: &BigUint) -> Option<BigUint> { 26 | let num_signed = BigInt::from(num.clone()); 27 | let mod_signed = BigInt::from(modulo.clone()); 28 | let (ext_gcd, _) = num_signed.extended_gcd_lcm(&mod_signed); 29 | if ext_gcd.gcd != BigInt::one() { 30 | None 31 | } else { 32 | let (sign, uint) = ext_gcd.x.into_parts(); 33 | debug_assert!(&uint < modulo); 34 | if sign == Sign::Minus { 35 | Some(modulo - uint) 36 | } else { 37 | Some(uint) 38 | } 39 | } 40 | } 41 | 42 | /// Computes the challenge for the Paillier encryption scheme. 43 | pub fn challenge<C: CurveGroup, D: Digest>( 44 | pubkey: &BigUint, 45 | vanishing_poly: &DensePolynomial<C::ScalarField>, 46 | ct_slice: &[BigUint], 47 | com_f_poly: &C, 48 | com_f_s_poly: &C, 49 | t_slice: &[BigUint], 50 | t: &C, 51 | ) -> BigUint { 52 | let mut hasher = Hasher::<D>::new(); 53 | hasher.update(pubkey); 54 | hasher.update(&vanishing_poly.coeffs); 55 | ct_slice.iter().for_each(|ct| hasher.update(ct)); 56 | hasher.update(com_f_poly); 57 | hasher.update(com_f_s_poly); 58 | t_slice.iter().for_each(|t| hasher.update(t)); 59 | hasher.update(t); 60 | 61 | BigUint::from_bytes_le(&hasher.finalize()) 62 | } 63 | 64 | #[cfg(test)] 65 | mod test { 66 | use super::super::server::Server; 67 | use super::super::N_BITS; 68 | use super::*; 69 | use ark_std::rand::distributions::Distribution; 70 | use ark_std::test_rng; 71 | use num_bigint::RandomBits; 72 | 73 | #[test] 74 | fn compute_modular_inverse() { 75 | let rng = &mut test_rng(); 76 | let server = Server::new(rng); 77 | let modulo = server.pubkey; 78 | let random_bits = RandomBits::new(N_BITS); 79 | for _ in 0..100 { 80 | let num: BigUint = 81 | <RandomBits as Distribution<BigUint>>::sample(&random_bits, rng) % &modulo; 82 | let inv = modular_inverse(&num, &modulo).unwrap(); 83 | assert_eq!((num * inv) % &modulo, BigUint::one()); 84 | } 85 | } 86 | } 87 | -------------------------------------------------------------------------------- /src/veck/mod.rs: -------------------------------------------------------------------------------- 1 | pub mod kzg; 2 | 3 | use ark_ff::FftField; 4 | use ark_poly::{EvaluationDomain, Evaluations, GeneralEvaluationDomain}; 5 | use ark_std::collections::HashMap; 6 | 7 | /// Maps the evaluation domain elements (roots of unity - keys) to their respective index (value) in the FFT domain. 8 | pub fn index_map<S: FftField>(domain: GeneralEvaluationDomain<S>) -> HashMap<S, usize> { 9 | domain.elements().enumerate().map(|(i, e)| (e, i)).collect() 10 | } 11 | 12 | /// Returns the indices of domain elements in the original domain, given they are also present in 13 | /// the subset domain. 14 | pub fn subset_indices<S: FftField>( 15 | index_map: &HashMap<S, usize>, 16 | subdomain: &GeneralEvaluationDomain<S>, 17 | ) -> Vec<usize> { 18 | subdomain 19 | .elements() 20 | .map(|e| *index_map.get(&e).unwrap()) 21 | .collect() 22 | } 23 | 24 | /// Returns the evaluations respective to the subdomain elements. 25 | pub fn subset_evals<S: FftField>( 26 | evaluations: &Evaluations<S>, 27 | indices: &[usize], 28 | subdomain: GeneralEvaluationDomain<S>, 29 | ) -> Evaluations<S> { 30 | debug_assert!(evaluations.domain().size() >= subdomain.size()); 31 | let mut subset_evals = Vec::<S>::new(); 32 | for &index in indices { 33 | subset_evals.push(evaluations.evals[index]); 34 | } 35 | Evaluations::from_vec_and_domain(subset_evals, subdomain) 36 | } 37 | 38 | /* 39 | // TODO some paillier subset toy examples https://github.com/PopcornPaws/fde/issues/9 40 | use crate::commit::kzg::Powers; 41 | use ark_ec::pairing::Pairing; 42 | use ark_ec::Group; 43 | use ark_poly::univariate::DensePolynomial; 44 | fn subset_pairing_check<C: Pairing>( 45 | phi: &DensePolynomial<C::ScalarField>, 46 | phi_s: &DensePolynomial<C::ScalarField>, 47 | domain: &GeneralEvaluationDomain<C::ScalarField>, 48 | subdomain: &GeneralEvaluationDomain<C::ScalarField>, 49 | powers: &Powers<C>, 50 | ) { 51 | let vanishing_poly = DensePolynomial::from(subdomain.vanishing_polynomial()); 52 | let quotient = &(phi - phi_s) / &vanishing_poly; 53 | let quotient_expected = (phi - phi_s) 54 | .divide_by_vanishing_poly(*subdomain) 55 | .unwrap() 56 | .0; 57 | assert_eq!(quotient, quotient_expected); 58 | // this only works with powers of tau 59 | //let com_q = powers.commit_g1(&quotient); 60 | //let com_f = powers.commit_g1(phi); 61 | //let com_f_s = powers.commit_g1(phi_s); 62 | //let com_v = powers.commit_g2(&vanishing_poly); 63 | //let lhs_pairing = C::pairing(com_q, com_v); 64 | //let rhs_pairing = C::pairing(com_f - com_f_s, C::G2::generator()); 65 | //assert_eq!(lhs_pairing, rhs_pairing); 66 | 67 | let phi_evals = phi.evaluate_over_domain_by_ref(*domain); 68 | let phi_s_evals = phi_s.evaluate_over_domain_by_ref(*domain); 69 | let q_evals = quotient.evaluate_over_domain_by_ref(*domain); 70 | let v_evals = vanishing_poly.evaluate_over_domain_by_ref(*domain); 71 | let com_q = powers.commit_scalars_g1(&q_evals.evals); 72 | let com_f = powers.commit_scalars_g1(&phi_evals.evals); 73 | let com_f_s = powers.commit_scalars_g1(&phi_s_evals.evals); 74 | let com_v = powers.commit_scalars_g2(&v_evals.evals); 75 | let lhs_pairing = C::pairing(com_q, com_v); 76 | let rhs_pairing = C::pairing(com_f - com_f_s, C::G2::generator()); 77 | assert_eq!(lhs_pairing, rhs_pairing); 78 | } 79 | 80 | 81 | fn subset_evals_zero_pad<S: FftField>( 82 | evaluations: &Evaluations<S>, 83 | sub_index_map: &HashMap<S, usize>, 84 | ) -> Evaluations<S> { 85 | let mut subset_evals = Vec::<S>::new(); 86 | for (x, eval) in evaluations.domain().elements().zip(&evaluations.evals) { 87 | if sub_index_map.contains_key(&x) { 88 | subset_evals.push(*eval); 89 | } else { 90 | subset_evals.push(S::zero()) 91 | } 92 | } 93 | Evaluations::from_vec_and_domain(subset_evals, evaluations.domain()) 94 | } 95 | 96 | #[cfg(test)] 97 | mod test { 98 | use super::*; 99 | use crate::tests::{BlsCurve, Scalar}; 100 | use ark_std::{test_rng, UniformRand}; 101 | 102 | const DATA_SIZE: usize = 4; 103 | const SUBSET_SIZE: usize = 2; 104 | 105 | #[test] 106 | fn mivan() { 107 | let rng = &mut test_rng(); 108 | let tau = Scalar::rand(rng); 109 | let powers = Powers::<BlsCurve>::unsafe_setup_eip_4844(tau, DATA_SIZE); 110 | 111 | let domain = GeneralEvaluationDomain::new(DATA_SIZE).unwrap(); 112 | let subdomain = GeneralEvaluationDomain::new(SUBSET_SIZE).unwrap(); 113 | 114 | let data = (0..DATA_SIZE).map(|_| Scalar::rand(rng)).collect(); 115 | let evaluations = Evaluations::from_vec_and_domain(data, domain); 116 | let im = index_map(domain); 117 | let sub_im = index_map(subdomain); 118 | let subset_evaluations = subset_evals(&evaluations, &im, subdomain); 119 | let subset_evaluations_zero_pad = subset_evals_zero_pad(&evaluations, &sub_im); 120 | 121 | let phi = evaluations.interpolate_by_ref(); 122 | let phi_s_expected = dbg!(subset_evaluations.interpolate_by_ref()); 123 | let phi_s = subset_evaluations_zero_pad.interpolate_by_ref(); 124 | subset_pairing_check(&phi, &phi_s, &domain, &subdomain, &powers); 125 | 126 | let r_scalars: Vec<Scalar> = (0..SUBSET_SIZE).map(|_| Scalar::rand(rng)).collect(); 127 | let t = powers.commit_scalars_g1(&r_scalars); 128 | let challenge = Scalar::rand(rng); 129 | let z_scalars: Vec<Scalar> = r_scalars 130 | .iter() 131 | .zip(&subset_evaluations.evals) 132 | .map(|(&r, &v)| r + challenge * v) 133 | .collect(); 134 | let com_f_s_poly = dbg!(powers.commit_scalars_g1(&subset_evaluations.evals)); 135 | let com_f_s_poly = dbg!(powers.commit_scalars_g1(&subset_evaluations_zero_pad.evals)); 136 | let commitment_pow_challenge = com_f_s_poly * challenge; 137 | let com_z = powers.commit_scalars_g1(&z_scalars); 138 | let t_expected = com_z - commitment_pow_challenge; 139 | assert_eq!(t, t_expected); 140 | } 141 | } 142 | */ 143 | --------------------------------------------------------------------------------