Abstract
This paper describes an algorithm for computing elliptic scalar multiplications on non-supersingular elliptic curves defined over GF(2m). The algorithm is an optimized version of a method described in [1], which is based on Montgomery’s method [8]. Our algorithm is easy to implement in both hardware and software, works for any elliptic curve over GF(2m), requires no precomputed multiples of a point, and is faster on average than the addition-subtraction method described in draft standard IEEE P1363. In addition, the method requires less memory than projective schemes and the amount of computation needed for a scalar multiplication is fixed for all multipliers of the same binary length. Therefore, the improved method possesses many desirable features for implementing elliptic curves in restricted environments.
Dept. of Computer Science, University of Valle, A.A. 25130 Cali, Colombia. Research supported by a CAPES-Brasil scholarship
Partially supported by a PRONEX-FINEP research grant no. 107/97
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López, J., Dahab, R. (1999). Fast Multiplication on Elliptic Curves Over GF(2m) without precomputation. In: Koç, Ç.K., Paar, C. (eds) Cryptographic Hardware and Embedded Systems. CHES 1999. Lecture Notes in Computer Science, vol 1717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48059-5_27
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