针对减宽SHA-1算法的模差分攻击分析  

Analysis of SHA-1 with reducing width for modular differential attack

作　　者：胡云山[1,2] 申意[1] 曾光[1] 韩文报[1,2] 

机构地区：[1]解放军信息工程大学,郑州450001 [2]数学工程与先进计算国家重点实验室,无锡214125

出　　处：《四川大学学报（自然科学版）》2016年第5期1041-1048,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：数学工程与先进计算国家重点实验室开放课题(2013A03;2013A10)

摘　　要：模差分攻击技术是SHA-1随机碰撞攻击中重要分析方法之一.针对减宽的SHA-1算法,该文得出了减宽的部分碰撞定理并给出了减宽SHA-1算法单一部分碰撞的概率,证明了模差分攻击技术同样适用于减宽的SHA-1算法.通过理论分析和计算机搜索,该文证明了对于宽为n比特的SHA-1算法,当且仅当n>3时,最优扰动向量的汉明重为25;当且仅当n>8时,最优扰动向量只有type-I与type-II两个等价类.Modular differential attack is one of the important methods in SHA-1 collision attacks. In allu- sion to width-reduced SHA-1 algorithm, the width-reduced local collisions theorems are deduced in this paper, and the probability of local collisions in width-reduced SHA-1 algorithm is proposed. Thus, modular differential attack is proved to be appropriate for width-reduced SHA-Ⅰ algorithm. By means of theoretical analysis and computer search, it is proved that for n-bit SHA-Ⅰ algorithm, the hamming weight of the optimum disturbance vector is 25 if and only if n〉3; and when and only when n〉8, the optimum disturbance vector has no other equivalence class than type- Ⅰ and type-Ⅱ.

关 键 词：密码学 HASH函数 SHA-1 模差分攻击 扰动向量 

分 类 号：TN918.1[电子电信—通信与信息系统]