SCALAR MULTIPLICATION ON HUFF CURVES USING THE FROBENIUS MAP
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
This paper introduces the scalar multiplication on Huff elliptic curves over a finite field using the Frobenius expansion. Applying the Frobenius endomorphism on Huff curve, we construct a Frobenius map defined on the quadratic twist of a Huff curve. To speed up the scalar multiplication on Huff curves, we use the GLV method combined with the Frobenius endomorphism over the curve.
Abstract
This paper introduces the scalar multiplication on Huff elliptic curves over a finite field using the Frobenius expansion. Applying the Frobenius endomorphism on Huff curve, we construct a Frobenius map defined on the quadratic twist of a Huff curve. To speed up the scalar multiplication on Huff curves, we use the GLV method combined with the Frobenius endomorphism over the curve.
참고문헌 (11)
- R. Avanzi, "Handbook of Elliptic and Hyperelliptic Cryptography", pp.2006, Chapman and Hall
- H. M. Edwards, "A normal form for elliptic curves", Bulletin of the American Mathe-matical Society, 44(3), pp.393~422 (2007)
- S. D. Galbraith, "Endomorphisms for faster elliptic curve cryptography on a large class of curves", J. Cryptology, 24(3), pp.446~469 (2011)
- R. P. Gallant, "Springer LNCS 2139", pp.190~200 (2001)
- 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)
- 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 Multiplicat", SCIS 2002, IEICE Japan, pp.699~702 (2002)
- M. Joye, "Hufis Model for Elliptic Curves, Algo-rithmic Number Theory - ANTS-IX", Lecture Notes in Computer Science, 6197, pp.234~250 (2010), Springer
- N. Koblitz, "Elliptic curve cryptosystems", Math. Comp, 48, pp.203~209 (1987)
- V. S. Miller, "Use of elliptic curves in cryptography", Ad-vances in Cryptology-CRYPTO'85, Lect. Notes Comput. Sci, 218, pp.417~426 (1986)
- D. Yong, "High speed modular divider based on GCD algorithm over GF(2m)", Journal of communications, 29(10), pp.199~204 (2008)