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02
Tue 二
Yi-Fu Lai Isogeny-based Cryptography
Lai and Maino, in their paper, propose efficient zkSNARK for isogeny-based cryptography using optimized Vélu formulas and theta model to encode various isogeny relations in R1CS, with applications to DeuringVRF signatures, SQISign, and POKÉ key validation, removing extra assumptions. Lai和Maino在论文中提出了面向同源密码的高效zkSNARK方案，通过优化Vélu公式和theta模型为多种同源关系提供R1CS编码，并展示了在DeuringVRF签名、SQISign和POKÉ密钥验证中的应用，移除了额外安全假设。
Key Points: 要点：
- • Existing ZKP for isogenies limited to small-degree chains, inefficient. 现有同源密码的ZKP局限于小次数同源链，效率低
- • Provide efficient R1CS for - and -isogenies and masked evaluations via optimized Vélu formulas. 利用优化的Vélu公式为 - 和 -同源及其掩码求值提供高效 R1CS 编码
- • Design R1CS for non-smooth isogenies of special degrees using theta model. 基于theta模型为特殊度数非光滑同源设计R1CS
- • Compiler removes 'one-more' evaluation assumption in DeuringVRF signatures. 构建编译器消除DeuringVRF签名中的“one-more”求值假设
- • Eliminate hint-based assumption in SQISign; conceptual key validation for POKÉ. 移除SQISign的提示假设，并概念性设计POKÉ密钥验证机制
- • Experimental proof sizes around 400 KB under NIST-1 primes. 实验显示在NIST-1素数下证明大小约400 KB