Constructions of involutions over finite fields

2018/11/28 by Zheng, Dabin, Yuan, Mu, Li, Nian +2 · 1 citation
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1811.11344

Abstract

An involution over finite fields is a permutation polynomial whose inverse is itself. Owing to this property, involutions over finite fields have been widely used in applications such as cryptography and coding theory. As far as we know, there are not many involutions, and there isn't a general way to construct involutions over finite fields. This paper gives a necessary and sufficient condition for the polynomials of the form x^rh(x^s)∈ \bF_q[x] to be involutions over the finite field~\bF_q, where r≥ 1 and s | (q-1). By using this criterion we propose a general method to construct involutions of the form x^rh(x^s) over \bF_q from given involutions over the corresponding subgroup of \bF_q^*. Then, many classes of explicit involutions of the form x^rh(x^s) over \bF_q are obtained.

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