一类非平衡Feistel网络的差分可证明安全性分析

该文深入研究了一类非平衡Feistel网络的差分可证明安全性。给出了其圈函数的具有非零差分概率的差分对应的结构形式。给出了连续m个非平凡差分对应的一个分布规律。证明了s(s2m)圈非平凡差分对应概率的上界为其轮函数非平凡差分对应概率最大值(pmax)的平方的2倍;当相应的轮函数为双射时,此上界可进一步改进为其轮函数非平凡差分对应概率的最大值的平方。最后对非平衡Feistel网络进行了讨论。

The Differential Provable Security Analysis of a Kind of Unbalanced Feistel Networks

The differential provable security of a kind of unbalanced Feistel networks is investigated deeply. The structure of the differential correspondence between round functions whose differential probability is nonzero is given. A distribution of m sequential differential correspondences is given. If pmax is the maximum of the probability of round function f(x), the upperbounds of the differential probability over at least 2m rounds is proven to be two times of the square of pmax and is proven to be the square of pmax when f(k, xm) is bijective. In conclusion, the unbalanced Feistel networks is discussed.