密码学报（中英文）2025，Vol.12Issue(2)：337-352,16.DOI:10.13868/j.cnki.jcr.000766
随机数泄露位置与模数对ECDSA安全性的影响
Impact of Nonces Leakage Location and Modulus on ECDSA Security
摘要
Abstract
Currently,the practical security analysis of elliptic curve digital signature algorithm(ECDSA)mostly involves constructing hidden number problems using random number information obtained through side channel attacks and then solving them.However,in theoretical research,the diversity of elliptic curve parameters and the uncertainty of obtaining random number information are often not taken into account,which may lead to inconsistent theoretical analysis results and actual solving effects for hidden number problems.This study conuducts experiments on the nonces leakage problem of ECDSA under different elliptic curve parameters and provides theoretical analysis based on Gaussian heuristic.It provides the usage method of recentering technique under different random number bit leakage conditions and proves that the success rate of solving the highest/middle bit leakage of random numbers is affected by modulus:the smaller the modulus,the lower the success rate of solving.Under the condition of a sample size of 70,highest/middle 4-bit nonce leakage,the success rate of solving is 90％ compared to using sm2p256v1 or secp256k1 elliptic curves,and 0％ when using brainpoolp256r1 elliptic curves.关键词
隐藏数问题/椭圆曲线数字签名算法/比特泄露问题/中心化技术Key words
hidden number problem/ECDSA/bits leak issues/tecentering technique分类
计算机与自动化引用本文复制引用
周呈景,王更,谷大武..随机数泄露位置与模数对ECDSA安全性的影响[J].密码学报（中英文）,2025,12(2):337-352,16.基金项目
国家密码科学基金(2025NCSF01005) （2025NCSF01005）
国家自然科学基金(U2336210)National Cryptologic Science Fund of China(2025NCSF01005) （U2336210）
National Natural Science Foundation of China(U2336210) （U2336210）
