Public key encryption and digital signatures based on permutation polynomials

Permutation polynomials over Z(n) form the basis of the RSA and Dickson public key schemes. Previously, however, only those permutation polynomials whose inverse permutation polynomial was easy to evaluate have been used in cryptography. The authors propose a way to avoid this restriction in public key cryptography by implementing secret key decryption and signature generation by computation of the gcd of two polynomials. This allows the implementation of new classes of public key scheme.