Twisted Hessian curves over the Ring F
DOI:
https://doi.org/10.5269/bspm.51867Abstract
Let Fq[e] be a ï¬nite ï¬eld 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 deï¬ne the Twisted Hessian curves Ha,d(Fq[e]) and we will show that HÏ€0(a),Ï€0(d)(Fq) and HÏ€1(a),Ï€1(d)(Fq) are two Twisted Hessian curves over the ï¬eld Fq, where Ï€0 and Ï€1 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 HÏ€0(a),Ï€0(d)(Fq)×HÏ€1(a),Ï€1(d)(Fq).
References
2. 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
3. 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
4. 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
5. 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
Downloads
Published
Issue
Section
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
