논문KCI 등재
Frobenius Endomorphisms of Binary Hessian Curves
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초록
This paper introduces the Frobenius endomophisms on the binary Hessian curves. It provides an efficient and computable homomorphism for computing point multiplication on binary Hessian curves. As an application, it is possible to construct the GLV method combined with the Frobenius endomorphism to accelerate scalar multiplication over the curve.
Abstract
This paper introduces the Frobenius endomophisms on the binary Hessian curves. It provides an efficient and computable homomorphism for computing point multiplication on binary Hessian curves. As an application, it is possible to construct the GLV method combined with the Frobenius endomorphism to accelerate scalar multiplication over the curve.
참고문헌 (14)
- R. Avanzi, "Handbook of Elliptic and Hyperelliptic Cryptography", pp.2006, Chapman and Hall
- D. Bernstein, "Twisted Hessian Curves", Proceedings of the 4th International Conference on Progress in Cryptology, LATINCRYPT 2015, 9230, pp.269~294 (2015)
- H. M. Edwards, "A normal form for elliptic curves", Bulletin of the American Mathematical Society, 44(3), pp.393~422 (2007)
- R. R. Farashahi, "Differential addition on binary elliptic curves", Finite fields and their applications, 87, pp.102141~ (2023)
- R. R. Farashahi, "Efficient arithmetic on Hessian curves", Public Key Cryptography-PKC 2010, 13th International Conference on Practice and Theory in Public Key Cryptography, pp.243~260 (2010)
- R. P. Gallant, "CRYPTO 2001", pp.190~200 (2001), Springer
- O. Hesse, "Uber die Elimination der variabeln aus drei algebraischen Gleichungen vom ¨zweiten Grade mit zwei Vaiabeln", Journal f¨ur die reine und angewandte Mathematik, 10, pp.68~96 (1844)
- G. B. Huff, "Diophantine problems in geometry and elliptic ternary forms", Duke Math. J., 15, pp.443~453 (1948)
- T. Iijima, "Construction of Frobenius Maps of Twists Elliptic Curves and its Application to Elliptic Scalar Multiplication", SCIS 2002, IEICE Japan, pp.699~702 (2002)
- M. Joye, "CHES 2001", pp.402~410 (2001), Springer
- N. Koblitz, "Elliptic curve cryptosystems", Math. Comp, 48, pp.203~209 (1987)
- V. S. Miller, "Advances in Cryptology-CRYPTO’85", pp.417~426 (1986)
- 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]
- 손교용, "SCALAR MULTIPLICATION ON HUFF CURVES USING THE FROBENIUS MAP", Advanced Studies in Contemporary Mathematics, 27(2), pp.223~228 (2017), 장전수학회[DOI]
관련 논문AI추천
EFFICIENT COMPUTABLE HOMOMORPHISMS ON HESSIAN CURVES손교용장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제1호Scalar multiplication on Jacobi curves using the Frobenius map손교용장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제1호SCALAR MULTIPLICATION ON HUFF CURVES USING THE FROBENIUS MAP손교용장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제2호SCALAR MULTIPLICATION ON GENERALIZED HUFF CURVES USING THE SKEW-FROBENIUS MAPGyoyong Sohn영남수학회 · East Asian Mathematical Journal2024 · 제40권 제5호WEAKNESSES OF THE TATE PAIRING ON GENERALIZED HESSIAN CURVESG. Y. Sohn장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제4호An algorithm for computing a sequence of Richelot isogeniesKatsuyuki Takashima, Reo Yoshida대한수학회 · 대한수학회보2009 · 제46권 제4호
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