基于最优区分器的多差分密码分析方法

Multiple Differential Cryptanalysis Based on Optimal Distinguisher

如何利用多个差分特征对分组密码算法进行差分攻击,从而精确地估计出分组密码算法抵抗差分攻击的能力,是一个重要的研究课题.文中基于最优区分器的思想,提出了一种多差分密码分析方法.针对每个实验密钥,构造出基于多个差分特征的统计量,根据统计量的大小判决实验密钥是否为正确密钥.给出了多差分分析方法的计算复杂度,分析了正确密钥、错误密钥对应统计量的概率分布规律,并在此基础上给出了多差分分析方法的成功率和数据复杂度之间的关系.通过具体实例表明,在成功率相同的条件下,基于的差分特征越多,需要的数据复杂度越小.

It is an important research topic to attack a block cipher using multiple differentials for exactly estimating the resistibility against differential cryptanalysis. In this paper, a multiple differential cryptanalysis method is proposed based on optimal distinguisher. For each experimental key, a statistic is constructed using multiple differentials, and thus we determine whether the experimental key is correct according to the statistics. We analyze the computational complexity of multiple differential cryptanalysis, the probability distribution of statistics corresponding correct key and incorrect key, and give the relation of success probability and data complexity. Example shows that the data complexity is decreased with more differentials in multiple differential cryptanalysis under the condition of same success probability.