diff --git a/basefold/basefold-01.md b/basefold/basefold-01.md index 1b35596..cdbb8c2 100644 --- a/basefold/basefold-01.md +++ b/basefold/basefold-01.md @@ -396,4 +396,8 @@ By recursively decomposing, we reach the base encoding $G_0$, which remains an R ## References -- [ZCF23] Zeilberger, H., Chen, B., Fisch, B. (2024). BaseFold: Efficient Field-Agnostic Polynomial Commitment Schemes from Foldable Codes. In: Reyzin, L., Stebila, D. (eds) Advances in Cryptology – CRYPTO 2024. CRYPTO 2024. Lecture Notes in Computer Science, vol 14929. Springer, Cham. \ No newline at end of file +- [ZCF23] Hadas Zeilberger, Binyi Chen, and Ben Fisch. "BaseFold: efficient field-agnostic polynomial commitment schemes from foldable codes." In *Annual International Cryptology Conference*, pp. 138-169. Cham: Springer Nature Switzerland, 2024. +- Riad S. Wahby, Ioanna Tzialla, Abhi Shelat, Justin Thaler, and Michael Walfish. "Doubly-efficient zkSNARKs without trusted setup." In *2018 IEEE Symposium on Security and Privacy (SP)*, pp. 926-943. IEEE, 2018. +- Tiancheng Xie, Jiaheng Zhang, Yupeng Zhang, Charalampos Papamanthou, and Dawn Song. "Libra: Succinct zero-knowledge proofs with optimal prover computation." In *Advances in Cryptology–CRYPTO 2019: 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18–22, 2019, Proceedings, Part III 39*, pp. 733-764. Springer International Publishing, 2019. +- Jiaheng Zhang, Tiancheng Xie, Yupeng Zhang, and Dawn Song. "Transparent polynomial delegation and its applications to zero knowledge proof." In *2020 IEEE Symposium on Security and Privacy (SP)*, pp. 859-876. IEEE, 2020. +- Charalampos Papamanthou, Elaine Shi, and Roberto Tamassia. "Signatures of correct computation." In *Theory of Cryptography Conference*, pp. 222-242. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. \ No newline at end of file diff --git a/basefold/basefold-01.zh.md b/basefold/basefold-01.zh.md index 53205ff..0899904 100644 --- a/basefold/basefold-01.zh.md +++ b/basefold/basefold-01.zh.md @@ -397,4 +397,8 @@ $$ ## References -- [ZCF23] Zeilberger, H., Chen, B., Fisch, B. (2024). BaseFold: Efficient Field-Agnostic Polynomial Commitment Schemes from Foldable Codes. In: Reyzin, L., Stebila, D. (eds) Advances in Cryptology – CRYPTO 2024. CRYPTO 2024. Lecture Notes in Computer Science, vol 14929. Springer, Cham. +- [ZCF23] Hadas Zeilberger, Binyi Chen, and Ben Fisch. "BaseFold: efficient field-agnostic polynomial commitment schemes from foldable codes." In *Annual International Cryptology Conference*, pp. 138-169. Cham: Springer Nature Switzerland, 2024. +- Riad S. Wahby, Ioanna Tzialla, Abhi Shelat, Justin Thaler, and Michael Walfish. "Doubly-efficient zkSNARKs without trusted setup." In *2018 IEEE Symposium on Security and Privacy (SP)*, pp. 926-943. IEEE, 2018. +- Tiancheng Xie, Jiaheng Zhang, Yupeng Zhang, Charalampos Papamanthou, and Dawn Song. "Libra: Succinct zero-knowledge proofs with optimal prover computation." In *Advances in Cryptology–CRYPTO 2019: 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18–22, 2019, Proceedings, Part III 39*, pp. 733-764. Springer International Publishing, 2019. +- Jiaheng Zhang, Tiancheng Xie, Yupeng Zhang, and Dawn Song. "Transparent polynomial delegation and its applications to zero knowledge proof." In *2020 IEEE Symposium on Security and Privacy (SP)*, pp. 859-876. IEEE, 2020. +- Charalampos Papamanthou, Elaine Shi, and Roberto Tamassia. "Signatures of correct computation." In *Theory of Cryptography Conference*, pp. 222-242. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. \ No newline at end of file diff --git a/basefold/basefold-02.md b/basefold/basefold-02.md index aecdd4f..0e92050 100644 --- a/basefold/basefold-02.md +++ b/basefold/basefold-02.md @@ -34,7 +34,7 @@ $$ This indicates that the folding process of the codeword does not disrupt the distance between the vector and the legitimate codeword space. By folding the vector sufficiently, the Verifier can use a very short code to verify whether the final folded vector is a legitimate codeword, thereby determining whether the original vector is a legitimate codeword. -> 📖 **Draft of Proximity Gap** +> 📖 **Notes on Proximity Gap** > Proof of Proximity utilizes a remarkable property of linear codes: the "Proximity Gap." Specifically, for two vectors $\pi, \pi'$, folding them with a random scalar $\alpha \in \mathbb{F}$ yields a set $A = \{\pi+\alpha\cdot \pi': \alpha \in \mathbb{F}\}$. Different $\alpha$ correspond to different elements in set $A$. The "Proximity Gap" theorem states that the elements in this set are either all close to the legitimate codeword space $C_{i}$ or only a negligible fraction of the elements are close to $C_{i}$, while the majority are at a distance of $\delta$ from $C_{i}$. In probabilistic terms: > @@ -247,4 +247,5 @@ This article described the framework of the Commit-phase and Query-phase of the ## References -- [ZCF23] Zeilberger, H., Chen, B., Fisch, B. (2024). BaseFold: Efficient Field-Agnostic Polynomial Commitment Schemes from Foldable Codes. In: Reyzin, L., Stebila, D. (eds) Advances in Cryptology – CRYPTO 2024. CRYPTO 2024. Lecture Notes in Computer Science, vol 14929. Springer, Cham. \ No newline at end of file +- [ZCF23] Zeilberger, H., Chen, B., Fisch, B. (2024). BaseFold: Efficient Field-Agnostic Polynomial Commitment Schemes from Foldable Codes. In: Reyzin, L., Stebila, D. (eds) Advances in Cryptology – CRYPTO 2024. CRYPTO 2024. Lecture Notes in Computer Science, vol 14929. Springer, Cham. +- [BCIKS20] Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, and Shubhangi Saraf. Proximity Gaps for Reed–Solomon Codes. In *Proceedings of the 61st Annual IEEE Symposium on Foundations of Computer Science*, pages 900–909, 2020. \ No newline at end of file diff --git a/basefold/basefold-02.zh.md b/basefold/basefold-02.zh.md index 46fb41d..f214811 100644 --- a/basefold/basefold-02.zh.md +++ b/basefold/basefold-02.zh.md @@ -32,7 +32,7 @@ $$ 这就说明了对 codeword 的折叠过程不会破坏向量与合法 codeword space 之间的距离，这个把向量折叠到足够小之后，Verifier 可以用极小的代码来验证折叠最后产生的向量是否是合法 codeword，从而可以得知原始向量是否是合法 codeword。 -> 📖 **Draft of Proximity Gap** +> 📖 **Notes on Proximity Gap** > Proof of Proximity 利用了线性编码的一个神奇性质：「Proximity Gap」，即对两个向量 $\pi, \pi'$ 用随机数 $\alpha \in \mathbb{F}$ 进行折叠得到一个集合 $A = \{\pi+\alpha\cdot \pi': \alpha \in \mathbb{F}\}$ ，不同的 $\alpha$ 就对应集合 $A$ 中不同的元素，那么 「Proximity Gap」结论告诉我们这个集合中的元素要么都距离合法的 codeword space $C_{i}$ 很近，要么只有极小极小部分元素距离合法的 codeword space $C_{i}$ 比较近，大部分的元素都距离 $C_{i}$ 有 $\delta$ 那么远。用概率表示即为 > > $$ @@ -243,4 +243,5 @@ $$ ## References -- [ZCF23] Zeilberger, H., Chen, B., Fisch, B. (2024). BaseFold: Efficient Field-Agnostic Polynomial Commitment Schemes from Foldable Codes. In: Reyzin, L., Stebila, D. (eds) Advances in Cryptology – CRYPTO 2024. CRYPTO 2024. Lecture Notes in Computer Science, vol 14929. Springer, Cham. +- [ZCF23] Hadas Zeilberger, Binyi Chen, and Ben Fisch. "BaseFold: efficient field-agnostic polynomial commitment schemes from foldable codes." Annual International Cryptology Conference. Cham: Springer Nature Switzerland, 2024. +- [BCIKS20] Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, and Shubhangi Saraf. Proximity Gaps for Reed–Solomon Codes. In *Proceedings of the 61st Annual IEEE Symposium on Foundations of Computer Science*, pages 900–909, 2020. diff --git a/basefold/basefold-03.md b/basefold/basefold-03.md index 9fa774b..6ae1763 100644 --- a/basefold/basefold-03.md +++ b/basefold/basefold-03.md @@ -476,4 +476,5 @@ At this point, we have obtained a Basefold Evaluation Argument protocol based on ## References -- [ZCF23] Hadas Zeilberger, Binyi Chen, and Ben Fisch. "BaseFold: efficient field-agnostic polynomial commitment schemes from foldable codes." Annual International Cryptology Conference. Cham: Springer Nature Switzerland, 2024. \ No newline at end of file +- [ZCF23] Hadas Zeilberger, Binyi Chen, and Ben Fisch. "BaseFold: efficient field-agnostic polynomial commitment schemes from foldable codes." Annual International Cryptology Conference. Cham: Springer Nature Switzerland, 2024. +- Jiaheng Zhang, Tiancheng Xie, Yupeng Zhang, and Dawn Song. "Transparent polynomial delegation and its applications to zero knowledge proof." In *2020 IEEE Symposium on Security and Privacy (SP)*, pp. 859-876. IEEE, 2020. \ No newline at end of file diff --git a/basefold/basefold-03.zh.md b/basefold/basefold-03.zh.md index 2bd071d..17128f0 100644 --- a/basefold/basefold-03.zh.md +++ b/basefold/basefold-03.zh.md @@ -466,4 +466,4 @@ $$ ## References - [ZCF23] Hadas Zeilberger, Binyi Chen, and Ben Fisch. "BaseFold: efficient field-agnostic polynomial commitment schemes from foldable codes." Annual International Cryptology Conference. Cham: Springer Nature Switzerland, 2024. -- \ No newline at end of file +- Jiaheng Zhang, Tiancheng Xie, Yupeng Zhang, and Dawn Song. "Transparent polynomial delegation and its applications to zero knowledge proof." In *2020 IEEE Symposium on Security and Privacy (SP)*, pp. 859-876. IEEE, 2020. \ No newline at end of file