Efficient Isogeny Proofs Using Generic Techniques
Efficient Isogeny Proofs Using Generic Techniques
复制标题
使用通用技术的有效同源性证明
DOI：
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Shai Levin
中科院分区：
文献类型：
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作者：
Kelong Cong;Yi;Shai Levin
。生成未知自同态环的超奇异椭圆曲线一直是困扰同源密码学家多年的问题。最近的一项发展提出了一种可信设置协议来生成这样的曲线，其中每个参与者都生成并证明了同源知识。因此，构造有效的同源知识证明引起了人们的新兴趣。从历史上看，同源社区一直认为从通用证明系统(如zkSNARK)获得知识的同源证明不是一种实用的方法。我们将Aurora(Eurocrypt‘19)、Ligero(CCS’17)和Limbo(CCS‘21)应用于同基因路径关系，并将它们的性能与相同关系的最新定制协议进行了比较，从而贡献了这一领域的第一个具体结果。在这样做的过程中，我们证明了现代通用证明系统在应用于同源假设时是有竞争力的，并且在证明和验证时间上提供了数量级(3-10×)的改进，并且具有相似的证明规模。此外，这些证明提供了更强的可靠性和统计零知识的概念；这一性质最近才在同源POK中实现。独立地说，这项技术在未来基于同源的协议或其他后量子协议的设计中显示出作为组件的前景。
. Generating supersingular elliptic curves of unknown endo-morphism ring has been a problem vexing isogeny-based cryptographers for several years. A recent development has proposed a trusted setup protocol to generate such a curve, where each participant generates and proves knowledge of an isogeny. Thus, the construction of efficient proofs of knowledge of isogeny has developed new interest. Historically, the isogeny community has assumed that obtaining isogeny proofs of knowledge from generic proof systems, such as zkSNARKs, was not a practical approach. We contribute the first concrete result in this area by applying Aurora (EUROCRYPT’19), Ligero (CCS’17) and Limbo (CCS’21) to an isogeny path relation, and comparing their performance to a state-of-the-art, tailor-made protocol for the same relation. In doing so, we show that modern generic proof systems are competitive when applied to isogeny assumptions, and provide an order of magnitude ( 3 - 10 × ) improvement to proof and verification times, with similar proof sizes. In addition, these proofs provide a stronger notion of soundness, and statistical zero-knowledge; a property that has only recently been achieved in isogeny PoKs. Independently, this technique shows promise as a component in the design of future isogeny-based or other post-quantum protocols.
DOI：
10.48550/arxiv.2205.00135
发表时间：
2022
期刊：
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影响因子：
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作者：
Booher J
通讯作者：
Booher J