ABOUT THE CHOICE OF THE IRREDUCIBLE POLYNOMIALS FOR THE SEA ALGORITHM


如何引用文章

全文:

详细

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.

参考

  1. Menezes A., van Oorchot P., Vanstone S. Handbook of applied cryptography. CRC Press, 1997. - 816 p.
  2. Ростовцев А. Г., Маховенко Е. Б. Два подхода к логарифмированию на эллиптической кривой. <http://www.ssl.stu.neva.ru/ssl/archieve/lift1.pdf>
  3. Atkin A.O.L., Morain F., Elliptic curves and primality proving // Math. Comp. 61, 203, 1993. - P. 339-405.
  4. 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.
  5. Elkies N.D. Explicit isogenies, manuscript // Boston, MA, 1992.
  6. Csirik J. A. An exposition of the SEA algorithm // Preprint, 2000. www.csirik.net/sch-survey.pdf <http://www.csirik.net/sch-survey.pdf>
  7. Menezes A., van Oorchot P., Vanstone S. Handbook of applied cryptography. CRC press, 1997. - 816 p.
  8. Blake I.F., Seroussi G., Smart N.P. Elliptic curves in cryptography. Cambridge Univ. Press, 1999. - 228 p.
  9. 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.
  10. 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.

补充文件

附件文件
动作
1. JATS XML

版权所有 © Babenko M.G., Chervyakov N.I., Babenko M.G., Chervaykov N.I., 2010

Creative Commons License
此作品已接受知识共享署名-非商业性使用-禁止演绎 4.0国际许可协议的许可。

##common.cookie##