Abstract:

Linear orthomorphisms have the good diffusibility, which can be used to design the P-permutation in the cryptography. The concept of the linear orthomorphisms and orthomorphic matrix on the residue class ring Z_n was proposed, and counting formulas of the linear orthomorphisms and orthomorphic matrix on the residue class modulo-n ring. It has provided a theoretical basis for the cryptographic research.

Key words:  the residue class ring; the linear orthomorphism; the orthomorphic matrix; the automorphism