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中文摘要：
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.
英文摘要：
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 with cryptologic properties beyond certain bound based on BCH code and Goppa code,at the same time this paper presents an novel algorithm. Finally,this paper finds one-to-one relationship between generated matrix of MDS code and the P-permutation with maximum branch number,further gives two kinds of methods based on Vandermonde matrix and Cauchy matrix to construct the P-permutation that has the maximum branch number,the P-permutation based on Vandermonde matrix is the special case of the P-permutation based on BCH code and Goppa code.
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