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Division polynomials for Huff's model of an elliptic curve

손교용
장전수학회 (Jangjeon Mathematical Society)|2013.01|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제16권 제1호|pp. 115-124|DOI 10.17777/pjms.2013.16.1.011

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참고문헌

키워드

Elliptic CurveHu 's ModelDivision Poly- nomial
주제분류수학

초록

This paper presents division polynomials for Huff model ofan elliptic curve. The division polynomials are important role for deter-mining the n-torsion torsion points on each curve. We also present thebasic properties and the speci c formulae for the division polynomialsof an elliptic curve.

Abstract

This paper presents division polynomials for Huff model ofan elliptic curve. The division polynomials are important role for deter-mining the n-torsion torsion points on each curve. We also present thebasic properties and the speci c formulae for the division polynomialsof an elliptic curve.

참고문헌 (14)

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  2. I. F. Blake, "Elliptic Curves in Cryptography", London Mathematical Society Lecture Note Series, 265 (1999)
  3. H. M. Edwards, "A normal form for elliptic curves", Bull. Am. Math. Soc., New Ser, 44(3), pp.393~422 (2007)
  4. S. Goldwaser, "Primality testing using elliptic curves", J. ACM, 46(4), pp.450~472 (1999)
  5. G. B. Huff, "Diophantine problems in geometry and elliptic ternary forms", Duke Math. J, 15, pp.443~453 (1948)
  6. N. Koblitz, "Elliptic curve cryptosystems", Math. Comp, 48, pp.203~209 (1987)
  7. H. W. Lenstra, Jr, "Factoring integers with elliptic curves", Ann. Math, 126(2) (1987)
  8. Marc Joye, "Huff's model for elliptic curves", 9th Algorithmic Number Theory Symposium (ANTS-IX) (2010)
  9. G. McGuire, "Two Kinds of Division Polynomials For Twisted Edward Curves"
  10. V. S. Miller, "Use of elliptic curves in cryptography, In H. C. Williams, editor, Advances in Cryptology-CRYPTO'85", Lect. Notes Comput. Sci, 218, pp.417~426 (1986)
  11. D. Moody, "Division Polynomials for Alternate Models of Elliptic Curves", ~ (2010)
  12. R. Moloney, "Division Polynomials for Twisted Edward Curves", ~ (2008)
  13. P. L. Mongomery, "Speeding up the Pollard and elliptic curve methods of factorization", Mathematics of Computation, 48(177), pp.243~264 (1987)
  14. L. C. Washington, "Elliptic Curves: Number Theory and Cryptography", pp.2003, Chapman & Hall

관련 논문AI추천

DIVISION POLYNOMIALS FOR TWISTED JACOBI INTERSECTIONS CURVES손교용장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호ON THE POINTS OF ELLIPTIC CURVES오장헌강원경기수학회 · 한국수학논문집2008 · 제16권 제4호Division polynomials for generalized binary Huff curvesG. Y. Sohn장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2014 · 제17권 제4호SCALAR MULTIPLICATION ON HUFF CURVES USING THE FROBENIUS MAP손교용장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제2호THE NUMBER OF POINTS ON ELLIPTIC CURVES y2 = x3 + Ax AND y2 = x3 + B3 MOD 24김대열, 전원주대한수학회 · 대한수학회논문집2013 · 제28권 제3호SCALAR MULTIPLICATION ON GENERALIZED HUFF CURVES USING THE SKEW-FROBENIUS MAPGyoyong Sohn영남수학회 · East Asian Mathematical Journal2024 · 제40권 제5호

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