Dickson Polynomials that are Involutions

Pascale Charpin; Sihem Mesnager; Sumanta Sarkar

Paper 2015/434

Dickson Polynomials that are Involutions

Pascale Charpin, 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.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Dickson polynomials permutation involution fixed point Jacobi symbol quadratic residue.
Contact author(s): sumanta sarkar @ gmail com
History: 2015-05-06: received
Short URL: https://ia.cr/2015/434
License: CC BY

BibTeX

@misc{cryptoeprint:2015/434,
      author = {Pascale Charpin and Sihem Mesnager and Sumanta Sarkar},
      title = {Dickson Polynomials that are Involutions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/434},
      year = {2015},
      url = {https://eprint.iacr.org/2015/434}
}