Construction and Count on Linear Orthomorphic Permutations Based on m Sequence

The orthomorphic permutation is a kind of one-to-one mapping from to F2. Orthomorphic permutations can be used in the constructions of nonlinear permutations in the cipher systems. In this paper, we show how to construct linear orthomorphic permutations by utilizing the trinomial property of m sequences. In our method, we only use m sequence, we can obtain all the maximal linear orthomorphic permutations and other linear orthomorphic permutations on F2, and this method can be implemented simply and easily.