Some Results on the Construction of Linear Orthomorphic Permutations

Orthomorphic permutations have many important applications in the design of block ciphers, hashing functions and pseudo-random sequence generators. The properties of a class of linear orthomorphic permutations are investigated in this paper, and the existence of integer l such that x + H(x) = H^l (x) is also studied, where H is an maximal linear orphic permutation. At last, we present an example to search the integer l that it satisfies the above condition, this method is only concerned m sequence, hence it is easily implemented.