A Note on the Constructions of Orthomorphic Permutations

Orthomorphic permutations have important applications in the design of block ciphers. A practical algorithm is derived to generate all orthomorphic permutations over F^m_2, and it is verified that the number of all orthomorphic permutations over F^4_2 is 244,744,192. With the theory of finite fields, a brief method is derived to generate a permutation polynomial corresponding to every permutation over F^m_2, and all orthomorphic permutation polynomials over F^4_2 are analyzed.