Cryptology ePrint Archive: Report 2015/434

Dickson Polynomials that are Involutions

Pascale Charpin and Sihem Mesnager and Sumanta Sarkar

Abstract: Dickson polynomials which are permutations are interesting combinatorial objects and well studied. In this paper, we describe Dickson polynomials of the first kind in $\mathbb{F}_2[x]$ that are involutions over finite fields of characteristic $2$. Such description is obtained using modular arithmetic's tools. We give results related to the cardinality and the number of fixed points (in the context of cryptographic application) of this corpus. We also present a class of Dickson involutions with high degree.

Category / Keywords: secret-key cryptography / Dickson polynomials, permutation, involution, fixed point, Jacobi symbol, quadratic residue.