Research on the Branch Number of P-permutation in Block Cipher
Huanguo Zhang · Journal of Chinese Computer Systems · 2010
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.