The Research on the Maximum Branch Number of P-Permutations

The P-permutation plays an important role in the round function of the block cipher, the MDS codes have been used to design the P-permutations with good characteristics in encryption-system for a long term. This paper finds two types of generated matrix of MDS codes viz. Vandermonde and Cauchy matrices, it gives two kinds of methods based on Vandermonde matrix and Cauchy matrix to construct good P-permutations that have lots of cryptographic usage, and generate the liner P-permutation over the extension field with maximum branch number by the other novel algorithms.