├── .gitignore
├── src
    ├── main.rs
    └── lib.rs
├── Cargo.toml
├── README.md
└── Cargo.lock


/.gitignore:
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1 | /target
2 | 


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/src/main.rs:
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1 | fn main() {
2 |     println!("Hello, world!");
3 | }
4 | 


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/Cargo.toml:
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 1 | [package]
 2 | name = "fhe-auctions"
 3 | version = "0.1.0"
 4 | edition = "2021"
 5 | 
 6 | # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 7 | 
 8 | [dependencies]
 9 | tfhe = {git = "https://github.com/Janmajayamall/tfhe-rs.git", features = ["boolean", "shortint", "integer", "p-encoding","aarch64-unix"]}
10 | rand = "0.8.5"


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/README.md:
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 1 | # FHE auctions
 2 | 
 3 | Implements bit slice approach for private auctions as described in [2002/189](https://eprint.iacr.org/2002/189).
 4 | 
 5 | Uses [tfhe-rs](https://github.com/zama-ai/tfhe-rs) to implement boolean gates using p-encoding technique as described in [2023/1589](https://eprint.iacr.org/2023/1589.pdf).
 6 | 
 7 | TFHE parameters are obtained via concrete-optimiser and has 128-bit of security.
 8 | 
 9 | # Costs
10 | 
11 | Auction circuit runtime increase linearly with $k$ and $n$, where $n$ is no. of bidders and $k$ is bits in bid (for ex, 64 bits, 128 bits)
12 | 
13 | Since a bid of $k$ bits is represented as $k$ LWE ciphertexts, each bidder needs to upload $k$ LWE ciphertexts.
14 | 
15 | # Test
16 | 
17 | On x86_64 based machines set `tfhe-rs` dependecy in cargo.toml as
18 | 
19 | `tfhe = {git = "https://github.com/Janmajayamall/tfhe-rs.git", features = ["boolean", "shortint", "integer", "p-encoding","x86_64-unix"]}`
20 | 
21 | On apple-silicon or aarch-64 based machines set `tfhe-rs` dependecy in cargo.toml as
22 | 
23 | `tfhe = {git = "https://github.com/Janmajayamall/tfhe-rs.git", features = ["boolean", "shortint", "integer", "p-encoding","aarch64-unix"]}`
24 | 
25 | then run `cargo test --release tests::auction_circuit_works -- --nocapture`
26 | 


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/src/lib.rs:
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  1 | use tfhe::gadget::{ciphertext::Ciphertext, server_key::ServerKey};
  2 | 
  3 | fn auction_circuit(
  4 |     server_key: &ServerKey,
  5 |     bids: &Vec<Vec<Ciphertext>>,
  6 |     bid_bits: usize,
  7 |     bidder_count: usize,
  8 | ) -> Result<(Vec<Ciphertext>, Vec<Ciphertext>), Box<dyn std::error::Error>> {
  9 |     //TODO: check bids are correctly formed
 10 | 
 11 |     let mut w = vec![Ciphertext::Trivial(true); bidder_count];
 12 |     let mut s = vec![Ciphertext::Placeholder; bidder_count];
 13 |     let mut amount = vec![Ciphertext::Placeholder; bid_bits];
 14 |     for i in 0..bid_bits {
 15 |         // let now = std::time::Instant::now();
 16 |         for j in 0..bidder_count {
 17 |             // AND at i^th MSB of j^th bidder
 18 |             s[j] = server_key.and(&w[j], &bids[j][i])?;
 19 |         }
 20 | 
 21 |         // OR
 22 |         let b = {
 23 |             let mut b = server_key.or(&s[0], &s[1])?;
 24 |             for j in 2..bidder_count {
 25 |                 b = server_key.or(&b, &s[j])?;
 26 |             }
 27 |             b
 28 |         };
 29 | 
 30 |         //  We require a multiplexer here and there are few ways to implement it:
 31 |         // 1. Circuit bootstrapping: Circuit bootstrap $b$ to a GGSW ciphertext and then use a single CMUX operation. However circuit bootstrapping itself requires $pbslevel$  bootstrapping operations + $pbslevel$ LWE -> RLWE key switching operations. Moreover, it requires private functional key switching keys. I don't think circuit bootstrapping improves runtime significantly such that it is worth it deal with its complexity + introducing more keys.
 32 |         // 2. Switch to 7-encoding space: In 7-encoding space this operation can be evaluated as single bootstrapping operation. However, p=7 requires 3 bit plaintext space thus doubling the bootstrapping runtime as compared to 2 bit plaintext space. Let bootstrapping runtime with 2-bit plaintext be x. Then evaluating AND + OR + MULTIPLEXER (MULTIPLEXER = $bs$ + $!bw$) takes 5x. With 3-bit plaintext space bootstrapping runtime equals 2x. Evaluating AND + OR + MULTIPLEXER (MULTIPLEXER is a single bootstrap) takes 5x. Thus, there's no benefit of switching to 7-encoding space.
 33 |         // 3. Rewriting multiplexer as $b * (s - w) + w$: This assumes ciphertexts are in canonical encoding (i.e. either 0/1 instead of 1/2). Switching from 1/2 to 0/1 is trivial since it requires a single plaintext subtraction by 1. However,  $s - w$ may equal -1 which will equal 2 in modulus 3. This forces lookup table to output to different values at same input (input: 1,0), which isn't possible.
 34 |         // 4. Naively implementation the multiplexer as $b s || !bw$: We implement this for now. However this requires 3 bootstrapping operations causing this to be the most expensive part of the circuit.
 35 |         // 5. Decrypting $b$: Since $b$ has to decrypted anyways to learn amount (assuming highest price auction), decrypting it before evaluating the multiplexer can save us from implementation it.
 36 |         // AND to reset w
 37 |         let b_not = server_key.not(&b);
 38 |         for j in 0..bidder_count {
 39 |             // (b & s[j]) + (!b & w[j])
 40 |             let c0 = server_key.and(&b, &s[j])?;
 41 |             let c1 = server_key.and(&b_not, &w[j])?;
 42 |             w[j] = server_key.or(&c0, &c1)?;
 43 |         }
 44 |         // println!("Time i:{i} - {}", now.elapsed().as_millis());
 45 |         // set i^th MSB of amount
 46 |         amount[i] = b;
 47 |     }
 48 | 
 49 |     Ok((w, amount))
 50 | }
 51 | 
 52 | #[cfg(test)]
 53 | mod tests {
 54 |     use rand::{thread_rng, Rng};
 55 |     use tfhe::gadget::{boolean::BOOLEAN_PARAMETERS, gen_keys};
 56 | 
 57 |     use super::*;
 58 | 
 59 |     #[test]
 60 |     fn auction_circuit_works() -> Result<(), Box<dyn std::error::Error>> {
 61 |         let bidders = 50;
 62 |         let BID_BITS = 64;
 63 | 
 64 |         let bids = (0..bidders)
 65 |             .into_iter()
 66 |             .map(|_| thread_rng().gen::<u64>())
 67 |             .collect::<Vec<u64>>();
 68 | 
 69 |         // generate FHE keys
 70 |         let (client_key, server_key) = gen_keys(&BOOLEAN_PARAMETERS);
 71 | 
 72 |         // encrypt bids
 73 |         let encrypts_bid_vector = bids
 74 |             .iter()
 75 |             .map(|bid_amount| {
 76 |                 // encrypt bits from MSB to LSB
 77 |                 (0..BID_BITS)
 78 |                     .into_iter()
 79 |                     .map(|i| {
 80 |                         let bit_i = (bid_amount >> (BID_BITS - 1 - i)) & 1;
 81 |                         client_key.encrypt(bit_i != 0)
 82 |                     })
 83 |                     .collect::<Vec<Ciphertext>>()
 84 |             })
 85 |             .collect::<Vec<Vec<Ciphertext>>>();
 86 | 
 87 |         let now = std::time::Instant::now();
 88 |         let (winner_identity_bit, winning_amount_bits) =
 89 |             auction_circuit(&server_key, &encrypts_bid_vector, BID_BITS, bidders)?;
 90 |         println!("Auction runtime: {}ms", now.elapsed().as_millis());
 91 | 
 92 |         // find the highest bidder amount
 93 |         let expected_highest_bid_amount = bids.iter().max().unwrap();
 94 |         let mut expected_highest_bidder_identity = vec![];
 95 |         bids.iter().enumerate().for_each(|(index, bid)| {
 96 |             if bid == expected_highest_bid_amount {
 97 |                 expected_highest_bidder_identity.push(index);
 98 |             }
 99 |         });
100 | 
101 |         // check correctness
102 |         // construct highest bidding amout returned from auction circuit
103 |         let mut res_highest_bid_amount = 0u64;
104 |         // winning amounts bits are stored from MSB to LSB
105 |         winning_amount_bits
106 |             .iter()
107 |             .enumerate()
108 |             .for_each(|(index, ct)| {
109 |                 let bit = client_key.decrypt(ct);
110 |                 res_highest_bid_amount =
111 |                     res_highest_bid_amount + ((bit as u64) << (BID_BITS - 1 - index));
112 |             });
113 | 
114 |         // find returned winner id
115 |         let mut res_highest_bidder_identity = vec![];
116 |         winner_identity_bit
117 |             .iter()
118 |             .enumerate()
119 |             .for_each(|(index, bit_ct)| {
120 |                 let bit = client_key.decrypt(bit_ct);
121 |                 if bit {
122 |                     res_highest_bidder_identity.push(index);
123 |                 }
124 |             });
125 | 
126 |         dbg!(expected_highest_bid_amount, res_highest_bid_amount);
127 |         dbg!(
128 |             &expected_highest_bidder_identity,
129 |             &res_highest_bidder_identity
130 |         );
131 | 
132 |         assert_eq!(*expected_highest_bid_amount, res_highest_bid_amount);
133 |         assert_eq!(
134 |             expected_highest_bidder_identity,
135 |             res_highest_bidder_identity
136 |         );
137 | 
138 |         Ok(())
139 |     }
140 | }
141 | 


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--------------------------------------------------------------------------------