Public Key Cryptography Using Permutation P-polynomials over Finite Fields

In this paper we propose an efficient multivariate public key cryptosystem based on permutation p-polynomials over finite fields. We first characterize a class of permutation ppolynomials over finite fields Fqm and then construct a trapdoor function using this class of permutation p-polynomials. The complexity of encryption in our public key cryptosystem is O(m) multiplication which is equivalent to other multivariate public key cryptosystems. However the decryption is much faster than other multivariate public key cryptosystems. In decryption we need O(m) left cyclic shifts and O(m) xor operations.