The binary operations calculus in H
DOI:
https://doi.org/10.5269/bspm.52539Abstract
Let Fq be a ï¬nite ï¬eld of q elements, where q is a power of a prime number p greater than or equal to 5, such that −3 is not a square in Fp. In this paper, we will study the twisted Hessian curve over the ring R2 = Fq[e], where the relation e^2 = 0. More precisely, we will give many various explicit formulas, which describe the binary operations calculus in H2a,d, where H2a,d is the twisted Hessian curve over R2, and we will reduce the cost of the complexity of the calculus in H2a,d.
References
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2. Lenstra, H. W, Eliptic Curves and Number-Theoretic Algorithms, Processing of the International Congress of Mathematicians, Berkely, California, USA, (1986).
3. N. Smart, The Hessian form of an elliptic curve. Cryptographic hardware and embedded systems-CHES 2001 (Paris), 118-125, Lecture Notes in Computer Science, 2162, Springer, Berlin, (2001). https://doi.org/10.1007/3-540-44709-1_11
4. A. Boulbot, A. Chillali and A. Mouhib, Elliptic Curves Over the Ring R, Bol. Soc. Paran,v. 38 3, pp 193-201, (2020). https://doi.org/10.5269/bspm.v38i3.39868
5. M. H. Hassib, A. Chillali, and M. A. Elomary, The Binary Calculus in Ea,b, Gulf Journal of Mathematics. Vol 8 p. 38-43, (2015).
6. 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
7. 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
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2022-02-07
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