본문 바로가기
KERD
논문KCI 등재

DIVISION POLYNOMIALS FOR TWISTED JACOBI INTERSECTIONS CURVES

손교용
장전수학회 (Jangjeon Mathematical Society)|2017.01|Advanced Studies in Contemporary Mathematics|제27권 제1호|pp. 73-84|DOI 10.17777/ascm2017.27.1.73

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Division PolynomialsTwisted Jacobi Intersections Curves
주제분류수학

초록

This paper presents two types of the division polynomials for twisted Jacobi intersections curves proposed by R. Feng et al. [7]. The division polynomials are important role for determining the n-torsion points of a given twisted Jacobi intersections curves. We also present the basic properties and the specific formulae for the division polynomials of a twisted Jacobi intersections curves.

Abstract

This paper presents two types of the division polynomials for twisted Jacobi intersections curves proposed by R. Feng et al. [7]. The division polynomials are important role for determining the n-torsion points of a given twisted Jacobi intersections curves. We also present the basic properties and the specific formulae for the division polynomials of a twisted Jacobi intersections curves.

참고문헌 (18)

  1. N. Abel, "Oeuvres Completes" (1881)
  2. A. O. L. Atkin, "Elliptic curves and primality proving", Math. Comp, 61(203), pp.29~68 (1993)
  3. I. F. Blake, "London Mathematical Society Lecture Note Series 265" (1999)
  4. O. Billet, "The Jacobi model of an elliptic curve and side-channel analysis, In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes 2003 proceed-ings", LNCS, 2643, pp.34~42 (2003), Springer
  5. D. V. Chudnovsky, "Sequences of numbers gnerated by addi-tion in formal groups and new primality and factorization tests", Advances in Applied Mathematics, 7, pp.385~434 (1986)
  6. H. M. Edwards, "A normal form for elliptic curves", Bull. Am. Math. Soc, 44(3), pp.393~422 (2007)
  7. R.Q. Feng, "Twisted Jacobi Intersections Curves, Theory and applications of models of computation", Lecture Notes in Computer Science, 6108, pp.199~210 (2010)
  8. S. Goldwaser, "Primality testing using elliptic curves", J. ACM, 46(4), pp.450~472 (1999)
  9. G. B. Hu, "Diophantine problems in geometry and elliptic ternary forms", Duke Math. J, 15, pp.443~453 (1948)
  10. M. Joye, "Hessian elliptic curves and side-channel attacks, InWork-shop on Cryptographic Hardware and Embedded systems proceedings", LNCS, 2162, pp.402~410 (2001), springer
  11. N. Koblitz, "Elliptic curve cryptosystems", Math. Comp, 48, pp.203~209 (1987)
  12. H. W. Lenstra, Jr, "Factoring integers with elliptic curves", Ann. Math, 126(2), pp.649~673 (1987)
  13. G. McGuire, "Two Kinds of Division Polynomials For Twisted Ed-ward Curves"
  14. G. McGuire, "Two Kinds of Division Polynomials For Twisted Edward Curves", Applicable Algebra in Engineering, Communication and Computing, 22(5-6), pp.321~345 (2011)
  15. V. S. Miller, "Use of elliptic curves in cryptography, In H. C. Williams, editor", Ad-vances in Cryptology-CRYPTO'85, Lect. Notes Comput. Sci, 218, pp.417~426 (1986)
  16. P. L. Mongomery, "Speeding up the Pollard and elliptic curve methods of factorization", Mathematics of Computation, 48(177), pp.243~264 (1987)
  17. D. Moody, "Division Polynomials for Alternate Models of Elliptic Curves", ~ (2010)
  18. L. C. Washington, "Elliptic Curves: Number Theory and Cryptography" (2003), Chapman &Hall

관련 논문AI추천

Division polynomials for Huff's model of an elliptic curve손교용장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2013 · 제16권 제1호Scalar multiplication on Jacobi curves using the Frobenius map손교용장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제1호EFFICIENT COMPUTABLE HOMOMORPHISMS ON HESSIAN CURVES손교용장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제1호STUDY ON THE JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES OVER FINITE FIELDS손교용장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제3호Jacobian Varieties of Hyperelliptic Curves over Finite Fields with the Formal Structure of the Mixed Type손교용영남수학회 · East Asian Mathematical Journal2021 · 제37권 제5호An algorithm for computing a sequence of Richelot isogeniesKatsuyuki Takashima, Reo Yoshida대한수학회 · 대한수학회보2009 · 제46권 제4호

이 간행물의 다른 논문 (13건)

ON A QUESTION OF SERGEI AKBAROVA. I. Shternpp. 1-6Weighted Adjacency Matrix of a Semigraph and its Spectral AnalysisN.Ravikumar, H.N. Ramaswamypp. 7-30SYMMETRIC IDENTITIES OF HIGHER-ORDER DEGENERATE q-BERNOULLI POLYNOMIALS김태균, 권혁인, 장관우pp. 31-42DECOMPOSING NORMED UNITS IN COMMUTATIVE MODULAR GROUP RINGSPeter V. Danchevpp. 43-48FOURIER SERIES OF FUNCTIONS RELATED TO BERNOULLI POLYNOMIALSToufik Mansour, 김태균, 김대산, 장관우pp. 49-62
원문 보기