Twisted Hessian curves over the Ring F

  • Elhamam Moha Ben Taleb Sidi Mohamed Ben Abdellah University
  • Abdelhakim CHILLALI Sidi Mohamed Ben Abdellah University http://orcid.org/0000-0002-2033-0280
  • Lhoussain El Fadil Sidi Mohamed Ben Abdellah University

Resumo

Let Fq[e] be a finite field of q elements, where q is a power of a prime number p. In this paper, we study the Twisted Hessian curves over the ring Fq[e], where e2 = e, denoted by Ha,d(Fq[e]); (a,d) ∈ (Fq[e])2. Using the Twisted Hessian equation, we define the Twisted Hessian curves Ha,d(Fq[e]) and we will show that Hπ0(a),π0(d)(Fq) and Hπ1(a),π1(d)(Fq) are two Twisted Hessian curves over the field Fq, where π0 and π1 are respectively the canonical projection and the sum projection of coordinates from Fq[e] to Fq. Precisely, we give a bijection between the sets Ha,d(Fq[e]) and Hπ0(a),π0(d)(Fq)×Hπ1(a),π1(d)(Fq). 

Downloads

Não há dados estatísticos.

Referências

Daniel J. Bernstein, Chitchanok Chuengsatiansup, David Kohel, and Tanja Lange, Twisted Hessian Curves, In LATINCRYPT 2015, pp 269-294, (2015).https://doi.org/10.1007/978-3-319-22174-8_15

A. Boulbot, A. Chillali and A. Mouhib, Elliptic Curves Over the Ring R, Bol. Soc. Paran,v. 38 3, pp 193-201, (2015). https://doi.org/10.5269/bspm.v38i3.39868

M. H. Hassib, A. Chillali, M. A. Elomary, Elliptic curves over a chain ring of characteristic 3, Journal of Taibah University for Science, 40(9), pages 1687-1700 (2015). https://doi.org/10.1016/j.jtusci.2015.02.001

M. Joye and J. Quisquater, V.L. Hessian elliptic curves and sidechannel attacks. Cryptographic Hardware and Embedded Systems - CHES 2001', Lecture Notes in Computer Science Vol,2162, Springer, pp. 402-410.(2010). https://doi.org/10.1007/3-540-44709-1_33

A. Tadmori, A. Chillali, M. Ziane, Elliptic Curve over Ring A4 = F d 2 [ε] , ε 4 = 0, Applied Mathematical Sciences, Volume 9, Issue 33, Pages 1721-1733(2015). https://doi.org/10.12988/ams.2015.5147

Publicado
2022-02-04
Seção
Proceedings