The Biggest B-Number to Cryptographic Linear P-Permutations

Abstract

A P-permutations have an crucial part in the round function of some famous block cipher. One important parameter to measure the quality of P- permutations is the branch number. Researchers have long established a consensus that MDS codes are used to design P-permutations, which will have a large branch number and good cryptography characteristics. The authors have found the two kinds of generated matrix to MDS-code, namely, which their generating matrices are known as the so-called Vandermonde＆Cauchy matrices. When these two classes of matrices are treated as linear P-permutations, the branch number reaches the maximum. They can be applied in cryptography system.