A New Public Key Encryption System Based on Permutation Polynomials

In this paper a new public key encryption and digital signature system based on permutation polynomials is developed. The permutation polynomial P(x) is replaced by P(xi) mod g(x) where g(x) is a secret primitive polynomial, i is the secret number such that (i, 2n-1) =1 and P(xi) = Pi(x) is declared to be a public polynomial for encryption. A public key encryption of given m(x) is the evaluation of polynomial Pi(x) at point m(x) where the result of evaluation is calculated via so called White box reduction, which does not reveal the underlying secret polynomial g(x). It is shown that for the new system to achieve a comparable security with conventional public key systems based on either Discrete logarithm or Integer factorization problems, substantially less processing length n is required resulting in a significant acceleration of public key operations.