A public key cryptosystem using a group of permutation polynomials

Abstract

In this paper we propose an efficient multivariate
public key cryptosystem based on permutation polynomials over
finite fields. We single out a commutative group $\mathfrak{L}(q,m)$ of permutation
polynomials over the finite field $F_{q^{m}}$. We construct a
trapdoor function for the cryptosystem using polynomials in $\mathfrak{L}(2,m)$, where $m=2^k$ for some $k\geq 0$.
The complexity of encryption in our public key cryptosystem is
$O(m^{3})$ multiplications which is equivalent to other
multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and
xor operations are used. It uses at most $5m^2-3m-6$ cyclic shifts,
$5m^2-3m+2$ xor operations and $6$ permutations on bits for decryption.