Email this article ABOUT THE CHOICE OF THE IRREDUCIBLE POLYNOMIALS FOR THE SEA ALGORITHM
- Authors: Babenko MG1, Chervyakov NI1, Babenko MG1, Chervaykov NI1
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- Issue: Vol 8, No 4 (2010)
- Pages: 4-9
- Section: Articles
- URL: https://journals.eco-vector.com/2073-3909/article/view/55665
- ID: 55665
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Abstract
The SEA algorithm for fi nding the number of points of an elliptic curve defi ned over a prime fi eld is analyzed in the article. In the case of «prime Atkin» is proposed to construct quadratic fi elds, the authors recommend the use of irreducible binomials, which allow the most effi cient to implement arithmetic in quadratic Galois fi eld.
References
- Menezes A., van Oorchot P., Vanstone S. Handbook of applied cryptography. CRC Press, 1997. - 816 p.
- Ростовцев А. Г., Маховенко Е. Б. Два подхода к логарифмированию на эллиптической кривой. <http://www.ssl.stu.neva.ru/ssl/archieve/lift1.pdf>
- Atkin A.O.L., Morain F., Elliptic curves and primality proving // Math. Comp. 61, 203, 1993. - P. 339-405.
- Elkies N.D. Elliptic and modular curves over finite fields and related computaional issues // Computational perspectives in number theory: Proc. of a Conf. in Honor of A.O. L.Atkin, J. T. Teitelbaum and D.A.Buell, editors. 1998. - P. 21-76.
- Elkies N.D. Explicit isogenies, manuscript // Boston, MA, 1992.
- Csirik J. A. An exposition of the SEA algorithm // Preprint, 2000. www.csirik.net/sch-survey.pdf <http://www.csirik.net/sch-survey.pdf>
- Menezes A., van Oorchot P., Vanstone S. Handbook of applied cryptography. CRC press, 1997. - 816 p.
- Blake I.F., Seroussi G., Smart N.P. Elliptic curves in cryptography. Cambridge Univ. Press, 1999. - 228 p.
- Joux A, Lercier R. «Chinese&Match», an alternative to Atkin's «Match and Sort» method used in the SEA algorithm // Mathematics of Computation. 70(234), 2001. - P. 827-836.
- Василенко О.Н. К вопросу о вычислении порядка группы точек эллиптической кривой над конечным простым полем // Труды по дискретной математике. Вып. 9. М.: Гелиос АРВ, 2006. - С. 32-50.
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