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EFFICIENT COMPUTABLE HOMOMORPHISMS ON HESSIAN CURVES

손교용
장전수학회 (Jangjeon Mathematical Society)|2020.01|Advanced Studies in Contemporary Mathematics|제30권 제1호|pp. 135-143

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참고문헌

키워드

Scalar MultiplicationFrobenius EndomorphismHessian Curve
주제분류수학

초록

This paper presents Frobenius endomorphisms on generalized Hessian curves and twisted Hessian curves. It gives an ecient computable homomorphism to compute the point multiplication on Hessian curve over a nite eld. As an application, we describe the GLV method combied with the Frobenius endomorphism over the curve to speed up the scalar multiplication.

Abstract

This paper presents Frobenius endomorphisms on generalized Hessian curves and twisted Hessian curves. It gives an ecient computable homomorphism to compute the point multiplication on Hessian curve over a nite eld. As an application, we describe the GLV method combied with the Frobenius endomorphism over the curve to speed up the scalar multiplication.

참고문헌 (20)

  1. R. Avanzi, "Handbook of Elliptic and Hyperelliptic Cryptography", pp.2006, Chapman and Hall
  2. D. Bernstein, "Twisted Hessian Curves", Proceedings of the 4th International Conference on Progress in Cryptology, LATINCRYPT 2015, 9230, pp.269~294 (2015)
  3. D. V. Chudnovsky, "Sequences of numbers generated by addition in formal groups and new primality and factorizaation tests", Advances in Applied Mathematics, 7(4), pp.385~434 (1986)
  4. H. M. Edwards, "A normal form for elliptic curves", Bulletin of the American Mathematical Society, 44(3), pp.393~422 (2007)
  5. R. R. Farashahi, "Efficient arithmetic on Hessian curves, in: Public Key Cryptography-PKC 2010", 13th International Conference on Practice and Theory in Public Key Cryptography, pp.243~260 (2010)
  6. S. D. Galbraith, "Endomorphisms for faster elliptic curve cryptography on a large class of curves", J. Cryptology, 24(3), pp.446~469 (2011)
  7. R. P. Gallant, "Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms", CRYPTO 2001, pp.190~200 (2001)
  8. J. Guajardo, "Itoh-tusji version in standard basis and its applicaiton in cryptography and codes", Design, Codes and Cryptography, 25(2), pp.207~216 (2002)
  9. O. Hesse, "Uber die Elimination der variabeln aus drei algebraischen Gleichungen vom zweiten Grade mit zwei Vaiabeln", Journal fur die reine und angewandte Mathematik, 10, pp.68~96 (1844)
  10. G. B. Huff, "Diophantine problems in geometry and elliptic ternary forms", Duke Math. J., 15, pp.443~453 (1948)
  11. T. Iijima, "Construction of Frobenius Maps of Twists Elliptic Curves and its Application to Elliptic Scalar Multiplication", SCIS 2002, pp.699~702 (2002)
  12. M. Joye, "Hessian elliptic curves and side-channel attacks", CHES 2001, pp.402~410 (2001), Springer
  13. A. Knapp, "Elliptic Curves" (1992), Princeton University Press
  14. N. Koblitz, "Elliptic curve cryptosystems", Math. Comp., 48, pp.203~209 (1987)
  15. V. S. Miller, "Use of elliptic curves in cryptography", Advances in Cryptology-CRYPTO'85, Lect. Notes Comput. Sci., 218, pp.417~426 (1986)
  16. J. H. Silverman, "The Arithmetic of Elliptic curves" (1986), Springer
  17. 손교용, "Scalar multiplication on Jacobi curves using the Frobenius map", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 22(1), pp.7~14 (2019), 장전수학회[DOI]
  18. 손교용, "SCALAR MULTIPLICATION ON HUFF CURVES USING THE FROBENIUS MAP", Advanced Studies in Contemporary Mathematics, 27(2), pp.223~228 (2017), 장전수학회[DOI]
  19. N. P. Smart, "The Hessian form of an elliptic curve", CHES 2001, pp.118~125 (2001), Springer
  20. D. Yong, "High speed modular divider based on GCD algorithm over GF(2m)", Journal of communications, 29(10), pp.199~204 (2008)

관련 논문AI추천

Frobenius Endomorphisms of Binary Hessian Curves손교용영남수학회 · East Asian Mathematical Journal2023 · 제39권 제5호SCALAR MULTIPLICATION ON GENERALIZED HUFF CURVES USING THE SKEW-FROBENIUS MAPGyoyong Sohn영남수학회 · East Asian Mathematical Journal2024 · 제40권 제5호SCALAR MULTIPLICATION ON HUFF CURVES USING THE FROBENIUS MAP손교용장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제2호Scalar multiplication on Jacobi curves using the Frobenius map손교용장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제1호WEAKNESSES OF THE TATE PAIRING ON GENERALIZED HESSIAN CURVESG. Y. Sohn장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제4호Tate pairing computation on the divisors of hyperelliptic curves of genus 2이윤진, Eunjeong Lee대한수학회 · 대한수학회지2008 · 제45권 제4호

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