Simple Permutation Ciphers Using Permutation Polynomials
G. R. Blakley, PF Stiller, Eiji Okamoto, Wayne Aitken · International Symposium on Information Theory and its Applications · 1994
A simple permutation cipher scheme using polynomials over a finite field is presented. Permutation, as well as substitution, plays a major role in almost all conventional cryptosystems. However the security of a permutation-based scheme depends on how the symbols are permuted. This paper investigates properties of polynomials which induce bijective functions, especially low degree polynomials, and proposes the use of these polynomials for permutation ciphers. Low degree polynomials are important for applications to permutation ciphers, because the degree of the polynomial is strongly related to the ostensible amount of randomness and security of the permutation cipher. The proposed permutation ciphers satisfy certain randomness and security criteria. The proposed permutation representation is very simple, but can provide random-appearing permutations.