Grouping Cipher Design Safety Parameters Analysis

In this paper , We mainly analyze several secure parameters in the design of block ciphers, including branch number of the SP-structure cipher, Algebraic degrees and the number of formal algebraic term.Branch number is an important parameter in the linear and differential cryptanalysis on block ciphers, In the first chapter , we mainly discuss the branch number of Rijndael. Firstly according to SP-graph , The algebraic structure of Rijndael is presented in detail, ShiftRows and MixColumns are made of a linear and reversible transformation: as a byte transformation, It can be regarded as a 16×16 metric transformation over GF(2~8) , as well as a 128x128 metric transformation over GF(2); Then on the premise of the knowledge of linear code and branch number, The result of achieving maximal branch number for Rijndael is proved in detail.In the second chapter , Basic algebraic cryptanalysis on Fly algorithm is given by writing equations as in algebraic cryptanalysis on Rijndael. For a pair of known plaintext and ciphertext, Algebraic degrees of equations on field GF(2~4) are presented ; also the number of formal algebraic term and linearly independent equations about quardratic equations on field GF(2) are presented : t=88i-432 and r =11i, Then the relationship and differences of such two types of equations are given.