知识的拟循环Stern证明
Quasi-Cyclic Stern Proof of Knowledge
摘要：
正在进行的NIST标准化过程表明，基于知识证明（PoK）的签名已成为可能的后量子签名的重要类型。关于基于代码的密码学，基于PoK的签名的原始方法是Stern协议，其允许证明小权重向量的知识，从而解决F2上的综合征解码（SD）问题的给定实例。它具有等于2/3的稳健性误差。几年后，Véron提出了一种基于一般综合征解码（GSD）问题的方案变体，从而在通信方面获得了更好的结果。几年后，AGS协议引入了基于准循环（QC）矩阵的Véron协议的变体。AGS协议允许获得1/2的渐近可靠性误差和通信方面的改进。在本文中，我们介绍了准循环斯特恩PoK，它构成了自适应的AGS计划在SD上下文中，以及几个新的优化代码为基础的PoK。我们的主要优化的签名的大小不能适用于GSD为基础的协议，如AGS，因此激励我们的新协议的设计。此外，我们还提供了一个特殊的合理性证明，这是兼容使用的菲亚特-沙米尔变换的5轮协议。这种方法不仅对我们的协议有效，而且对缺乏这种证明的AGS协议也有效。我们比较我们的结果与现有的签名，包括最近的基于代码的签名的基础上PoK利用MPC的头部范例。在实践中，我们的新协议与AGS一样快，同时将其相关签名长度减少了20%。因此，它构成了一个有趣的权衡签名长度和执行时间的设计基于代码的签名只依赖于SD问题的难度。
英文摘要：
The ongoing NIST standardization process has shown that Proof of Knowledge (PoK) based signatures have become an important type of possible post-quantum signatures. Regarding code-based cryptography, the original approach for PoK based signatures is the Stern protocol which allows to prove the knowledge of a small weight vector solving a given instance of the Syndrome Decoding (SD) problem over F2. It features a soundness error equal to 2/3. This protocol was improved a few years later by Véron who proposed a variation of the scheme based on the General Syndrome Decoding (GSD) problem which leads to better results in term of communication. A few years later, the AGS protocol introduced a variation of the Véron protocol based on Quasi-Cyclic (QC) matrices. The AGS protocol permits to obtain an asymptotic soundness error of 1/2 and an improvement in term of communications. In the present paper, we introduce the Quasi-Cyclic Stern PoK which constitutes an adaptation of the AGS scheme in a SD context, as well as several new optimizations for code-based PoK. Our main optimization on the size of the signature can't be applied to GSD based protocols such as AGS and therefore motivated the design of our new protocol. In addition, we also provide a special soundness proof that is compatible with the use of the Fiat-Shamir transform for 5-round protocols. This approach is valid for our protocol but also for the AGS protocol which was lacking such a proof. We compare our results with existing signatures including the recent code-based signatures based on PoK leveraging the MPC in the head paradigm. In practice, our new protocol is as fast as AGS while reducing its associated signature length by 20%. As a consequence, it constitutes an interesting trade-off between signature length and execution time for the design of a code-based signature relying only on the difficulty of the SD problem.
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