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 polynomialspermutationinvolutionfixed pointJacobi symbolquadratic residue.
Contact author(s)
sumanta sarkar @ gmail com
History
2015-05-06: received
Short URL
https://ia.cr/2015/434
License
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2015/434}},
      url = {https://eprint.iacr.org/2015/434}
}
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