密码学报（中英文）2025，Vol.12Issue(2)：322-336,15.DOI:10.13868/j.cnki.jcr.000765
同源密码学中的光滑离散对数计算
Smooth Discrete Logarithm Computation in Isogeny-Based Cryptography
摘要
Abstract
As a branch of post-quantum cryptography,isogeny-based cryptography has been widely concerned by cryptographers because of its extremely short public key size.Most isogeny-based schemes involve discrete logarithm computations.To speed up discrete logarithm computation,bilinear pairings are employed to transform them into discrete logarithm computation over finite fields.However,the state-of-the-art requires relatively large storage.This study proposes new algorithms to compute discrete logarithms in isogeny-based cryptography.By leveraging the special structure of the group,the new algorithms avoid extensive precomputation and simplify smooth discrete logarithm computations via Lucas sequences.In the parameter settings of SQIsignHD,the computational cost of the proposed algorithm is about 1.5 times that of the current algorithms,but the storage requirements are only 4.47％ 12.89％ of the current algorithms'.关键词
后量子密码学/同源密码学/光滑离散对数计算/Pohlig-Hellman算法Key words
post-quantum cryptography/isogeny-based cryptography/smooth discrete logarithm computation/Pohlig-Hellman algorithm分类
计算机与自动化引用本文复制引用
林楷展,王林,王维则,赵昌安..同源密码学中的光滑离散对数计算[J].密码学报（中英文）,2025,12(2):322-336,15.基金项目
国家自然科学基金(12441107)National Natural Science Foundation of China(12441107) （12441107）
