分组密码中P-置换的分支数研究

P-置换是分组密码轮函数的重要组成部分,好的P-置换能使得轮函数具有更强的抵抗线性和差分攻击能力,长期以来人们利用MDS码设计出了密码性质优良的P-置换,然而在有些情况下,P-置换本的密码学性质只要不低于一个指定的界限,就能方便地应用,因此本文决定利用BCH码和Goppa码来设计密码学指标不低于指定值的P-置换,同时设计了相应算法.因为MDS码的生成矩阵与分支数最大的P-置换之间有一一对应关系,本文利用范德蒙矩阵和柯西矩阵的特性生成了两类分支数达到最大P-置换,最后本文指出利用范德蒙矩阵设计的P-置换是利用Goppa码来设计P-置换的特例.

Research on the Branch Number of P-permutation in Block Cipher

The P-permutation plays an important role in the round function of block ciphers,the well-designed P-permutation has a wonderful performance to resist differential and linear cryptanalysis. For long time,the Maximum Distance Separable codes (MDS) have been used to design the P-permutation with good characteristic in encryption-system. But sometimes the P-permutation will be utilized successfully so as its cryptographic properties are beyond certain bound. Herewith this paper has designed the P-permutation w...