├── .github ├── pull_request_template.md └── workflows │ ├── escape_markdown.sh │ └── notify.yml ├── .gitignore ├── CONTRIBUTING.md ├── README.md ├── analysis ├── basefold-analysis.md ├── basefold-analysis.zh.md ├── basefold-deepfold-whir.md ├── basefold-deepfold-whir.zh.md ├── gemini-analysis.md ├── gemini-analysis.zh.md ├── img │ ├── basefold-analysis-IOPP-query.png │ ├── basefold-analysis-encoding-algorithm.png │ ├── basefold-analysis-protocol.png │ ├── basefold-deepfold-whir-bound.svg │ ├── basefold-deepfold-whir-compare.svg │ ├── basefold-deepfold-whir-list-decoding.svg │ ├── basefold-deepfold-whir-whir.svg │ ├── zeromorph-fri-analysis-fri-query.svg │ ├── zeromorph-fri-analysis-fri-verify.svg │ └── zeromorph-fri-analysis-query.svg ├── ph23-analysis.md ├── ph23-analysis.zh.md ├── zeromorph-anlysis.md ├── zeromorph-anlysis.zh.md ├── zeromorph-fri-analysis.md └── zeromorph-fri-analysis.zh.md ├── basefold ├── README.md ├── basefold-01.md ├── basefold-01.zh.md ├── basefold-02.md ├── basefold-02.zh.md ├── basefold-03.md ├── basefold-03.zh.md ├── basefold-04.md ├── basefold-04.zh.md ├── basefold-05.md ├── basefold-05.zh.md ├── basefold-habock-overview.md ├── basefold-habock-overview.zh.md ├── basefold-habock-soundness.md ├── basefold-habock-soundness.zh.md ├── basefold-notebook.ipynb ├── basefold-opt.md ├── basefold-opt.zh.md ├── basefold-simple-version │ ├── Basefold-simple-version-img │ │ ├── image 1.png │ │ ├── image 2.png │ │ ├── image 3.png │ │ ├── image 4.png │ │ ├── image 5.png │ │ ├── image 6.png │ │ ├── image 7.png │ │ ├── image 8.png │ │ ├── image 9.png │ │ └── image.png │ └── Basefold-simple-version.md └── img │ ├── basefold-05-badnode.svg │ ├── basefold-05-binarytree.svg │ ├── basefold-05-coset-distance.svg │ ├── basefold-05-coset-example.svg │ ├── basefold-05-delta-reject.svg │ ├── basefold-05-delta.svg │ ├── basefold-habock-commit-map.svg │ ├── basefold-habock-commit-phase-1.svg │ ├── basefold-habock-commit-phase-2.svg │ ├── basefold-habock-commit-phase-3.svg │ ├── basefold-habock-commit-sumcheck.svg │ ├── basefold-habock-query.svg │ └── inter-poly.png ├── batch-export.py ├── coding-theory ├── List-Decoding-Algorithms.ipynb ├── List-Decoding.ipynb ├── Reed-Solomon-Codes.ipynb ├── Shannon-Theorem.ipynb ├── Unique-Decoding-Algorithm.ipynb └── imgs │ ├── image_bad_examples.png │ ├── image_bec.png │ ├── image_bsc.png │ ├── image_channel_diagram.png │ ├── image_unique_decoding_1.png │ └── image_unique_decoding_2.png ├── export-pdf.sh ├── fft ├── README.md └── reversed-bit-order.md ├── final-report.md ├── final-report.zh.md ├── fri-binius ├── README.md ├── binius-01.md ├── binius-01.zh.md ├── binius-02.md ├── binius-02.zh.md └── img │ ├── image-1.png │ ├── image-2.png │ ├── image.png │ └── subspace-1.png ├── fri ├── BBHR18-FRI.md ├── BBHR18-FRI.zh.md ├── BCIKS20-proximity-gaps.md ├── BCIKS20-proximity-gaps.zh.md ├── README.md ├── deepfold.md ├── deepfold.zh.md ├── fri-proximity-gap.md ├── fri-proximity-gap.zh.md ├── img │ ├── BBHR18-FRI-EXY.svg │ ├── BBHR18-FRI-fri3.png │ ├── BBHR18-FRI-fri_recrsion.png │ ├── BBHR18-FRI-function_log_sqrt.png │ ├── BBHR18-FRI-tosscoin-1.png │ ├── BBHR18-FRI-tosscoin-2.png │ ├── BCIKS20-proximity-gaps-several.svg │ ├── BCIKS20-proximity-gaps-within.svg │ ├── deepfold-correctness.svg │ ├── deepfold-deep.svg │ ├── deepfold-list-decoding.svg │ ├── deepfold-split-fold-deepfold.svg │ ├── deepfold-sumcheck-split-fold.svg │ ├── deepfold-sumcheck.svg │ ├── fri-proximity-affine-space.svg │ ├── fri-proximity-gap-3D.svg │ ├── fri-proximity-gap-binary.svg │ ├── fri-proximity-gap-check.svg │ ├── fri-proximity-gap-correlated-agreement.svg │ ├── fri-proximity-gap-f.svg │ ├── fri-proximity-gap-fold.svg │ ├── fri-proximity-gap-relation.svg │ ├── fri-proximity-gap-soundness.svg │ ├── fri-proximity-random-choose.svg │ ├── stir-FRI-STIR.svg │ ├── stir-comparison.png │ ├── stir-evaluation-domain.svg │ ├── stir-iopp-for-RS.excalidraw.svg │ ├── stir-iteration.svg │ ├── stir-out-of-domain-sampling.svg │ ├── stir-quotient.svg │ ├── whir-correlated-agreement.svg │ ├── whir-mutual-correlated-agreement.svg │ ├── whir-stir-iteration.svg │ └── whir.svg ├── stir.en.md ├── stir.zh.md ├── whir.md └── whir.zh.md ├── gemini ├── Gemini-PCS-1.md ├── Gemini-PCS-1.zh.md ├── Gemini-PCS-2.md ├── Gemini-PCS-2.zh.md ├── Gemini-PCS-3.md ├── Gemini-PCS-3.zh.md ├── Gemini-PCS-4.md ├── Gemini-PCS-4.zh.md ├── README.md ├── gemini-fri.md ├── gemini-fri.zh.md ├── gemini_01.ipynb ├── hyperkzg-pcs-01.md ├── hyperkzg-pcs-01.pdf ├── hyperkzg-pcs-01.zh.md ├── hyperkzg.ipynb └── image │ ├── Gemini-PIOP.png │ ├── Gemini-multipoly.png │ ├── Gemini-unipoly.png │ └── mle.png ├── grey-hound ├── greyhound_pcs.md └── greyhound_pcs.zh.md ├── hyrax-pcs ├── README.md ├── hyrax-01.md └── hyrax-01.zh.md ├── img ├── image.png ├── lattice.png └── zksnark.png ├── kzg10 ├── kzg notes │ ├── kzg-soundness-1.md │ ├── kzg-soundness-1.zh.md │ ├── kzg-soundness-2.md │ ├── kzg-soundness-2.zh.md │ ├── schnorr.png │ └── special_sound.png ├── kzg_hiding.md ├── kzg_hiding.zh.md └── rust_implementation │ ├── .gitignore │ ├── Cargo.toml │ └── src │ ├── kzg10.rs │ └── main.rs ├── libra-pcs ├── README.md ├── libra-pcs.md └── libra-pcs.zh.md ├── ligerito-pcs ├── ligerito-01.md └── ligerito-01.zh.md ├── math ├── field_ext_inverse.md ├── field_ext_inverse.zh.md ├── mle_div.md ├── mle_div.zh.md ├── newton_it.png ├── reductions │ ├── logjump_reduction.ipynb │ └── montgomery_reduction.ipynb ├── unipoly_div.md ├── unipoly_div.zh.md └── unipolynomial.py ├── mercury ├── img │ ├── mercury-batched-kzg.svg │ ├── mercury-compose.svg │ ├── mercury-decompose.svg │ ├── mercury-decomposing-univariate.svg │ ├── mercury-decomposing.svg │ ├── mercury-degree-bound.svg │ ├── mercury-full.svg │ ├── mercury-h-alpha.svg │ ├── mercury-h.svg │ ├── mercury-inner-product.svg │ ├── mercury-multi-to-univariate.svg │ ├── mercury-prove.svg │ └── mercury-send-value.svg ├── mercury-01.md ├── mercury-01.zh.md ├── mercury-02.md └── mercury-02.zh.md ├── mmcs ├── interpretions │ ├── .gitignore │ ├── book.toml │ └── src │ │ ├── SUMMARY.md │ │ ├── imgs │ │ ├── matrices.png │ │ ├── merkle_tree.png │ │ └── mmcs.png │ │ ├── merkle_tree.md │ │ └── mmcs.md └── rust │ ├── merkle_tree.rs │ └── mmcs.rs ├── ph23 ├── README.md ├── ph23-pcs-01.md ├── ph23-pcs-01.zh.md ├── ph23-pcs-02.md ├── ph23-pcs-02.zh.md ├── ph23-pcs-fri-01.md ├── ph23-pcs-fri-01.zh.md ├── ph23-pcs-fri-02.md ├── ph23-pcs-fri-02.zh.md ├── ph23-pcs-zk.md ├── ph23-pcs-zk.zh.md └── ph23.ipynb ├── poly-commit-rs ├── .gitignore ├── Cargo.toml └── src │ ├── lib.rs │ ├── libraries │ ├── mle.rs │ ├── mod.rs │ ├── unipolynomial.rs │ └── utils.rs │ ├── main.rs │ └── schemes │ └── mod.rs ├── publications └── Compressed_Sigma_from_Sumcheck.pdf ├── reductions ├── README.md ├── barrett.md ├── barrett.zh.md ├── montgomery.md └── montgomery.zh.md ├── src ├── Basefold.ipynb ├── Basefold.py ├── README.md ├── basefold_pcs.py ├── basefold_pcs_partial.py ├── basefold_rs_opt_pcs.py ├── basefold_rs_pcs.py ├── batch_fri.py ├── bcho_pcs.ipynb ├── bcho_pcs.py ├── circle.ipynb ├── circle.py ├── curve.py ├── deepfold.ipynb ├── deepfold_pcs.py ├── dp23_pcs.py ├── ff │ ├── babybear.py │ ├── goldilocks.py │ ├── koalabear.py │ ├── mersenne31.py │ └── tiny.py ├── field.py ├── fri.py ├── fri_babybear.py ├── group.py ├── hyperkzg_pcs.py ├── hyrax_pcs.py ├── ipa.py ├── kzg10.ipynb ├── kzg10.py ├── kzg10_hiding_m.py ├── kzg10_hiding_z.py ├── kzg10_non_hiding.py ├── kzg10_non_hiding2.py ├── kzg_hiding.py ├── libra_pcs.py ├── ligerito.ipynb ├── ligerito_pcs.py ├── mercury_pcs.ipynb ├── mercury_pcs.py ├── merkle.py ├── merlin │ ├── keccak.py │ ├── merlin_transcript.py │ └── strobe.py ├── mle2.py ├── mmcs.py ├── ph23_pcs.py ├── poetry.lock ├── pyproject.toml ├── samaritan_pcs.py ├── stir.ipynb ├── transcript.py ├── unipoly.py ├── unipoly2.py ├── unipolynomial.py ├── utils.py ├── whir_pcs.ipynb ├── whir_pcs.py ├── zeromorph.ipynb ├── zeromorph.py └── zeromorph_zk.py ├── test_all.sh ├── tests ├── test_Basefold.py ├── test_basefold_opt.py ├── test_basefold_pcs.py ├── test_batch_fri.py ├── test_circle.py ├── test_deepfold_opt.py ├── test_field.py ├── test_fri.py ├── test_fri_babybear.py ├── test_group.py ├── test_kzg10.py ├── test_kzg_hiding.py ├── test_merkle.py ├── test_mle2.py ├── test_mmcs.py ├── test_unipolynomial.py └── test_utils.py ├── typora-export-pdf.applescript ├── update-gh-pages.sh ├── virgo-pcs ├── README.md ├── virgo-pcs-01.md └── virgo-pcs-01.zh.md ├── whir-pcs ├── whir.md └── whir.zh.md └── zeromorph ├── README.md ├── img ├── image-1.png ├── image-2.png ├── image-3.png ├── image-6.png ├── image.png ├── zeromorph-fri-fold.svg ├── zeromorph-fri-mmcs.svg ├── zeromorph-fri-query.svg └── zeromorph-fri-verify.svg ├── implementation ├── .gitignore ├── Cargo.toml └── src │ └── main.rs ├── zeromorph-02.md ├── zeromorph-02.zh.md ├── zeromorph-fri.md ├── zeromorph-fri.zh.md ├── zeromorph.md ├── zeromorph.zh.md └── 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