对SMS4密码算法改进的差分攻击

差分分析和线性分析是重要的密码算法分析工具.多年来，很多研究者致力于改善这两种攻击方法.Achiya Bar-On等人提出了一种方法，能够使攻击者对部分状态参与非线性变换的SPN结构的密码算法进行更多轮数的差分分析和线性分析.这种方法使用了两个辅助矩阵，其目的就是更多地利用密码算法中线性层的约束，从而能攻击更多轮数.将这种方法应用到中国密码算法SMS4的多差分攻击中，获得了一个比现有攻击存储复杂度更低和数据复杂度更少的攻击结果.在成功概率为0.9时，实施23轮的SMS4密钥恢复攻击需要2^113.5个明文，时间复杂度为2^126.7轮等价的23轮加密.这是目前为止存储复杂度最低的攻击，存储复杂度为2¹⁷个字节.

Improved Differential Attack on 23-Round SMS4

For years, many cryptanalysts have been devoted to working on analyzing the security of block ciphers against differential attacks and linear attacks. Thus, there are copious methods to cryptanalyze a block cipher with differential and linear cryptanalyses. An original method proposed by Achiya Bar-On et al. enables attackers to analyze more rounds of a partial SPN network in differential and linear cryptanalyses. The method involves two auxiliary matrices, which makes it possible that more constraints on differences can be exploited to sieve the inappropriate pairs. In the paper, the method is implemented to SMS4 in the setting of a multiple differential cryptanalysis. By utilizing the 2¹⁴ existing 19-round differential characteristics, the paper carries out a 23-round key-recovery attack on SMS4, which leads to a lower data and memory complexities than previous multiple differential attack results on 23-round SMS4, namely,2^113.5 chosen plaintexts and 2¹⁷ bytes at a success possibility of 0.9. The attack presented in the paper can recover 128-bit key within 2^126.7 equivalent 23-round encryptions.