Abstract. This paper describes an algorithm for computing elliptic scalar multiplications on non-supersingular elliptic curves de ned over GF(2 m ). 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(2 m ), 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 xed for all multipliers of the same binary length. Therefore, the improved method possesses many desirable features for implementing elliptic curves in restricted environments.
The prototype performs point multiplication based on Montgomery Scalar Multiplication in projective space REF for GF (2 167 ).
Fast multiplication on elliptic curves over GF(2m) without precomputation
CHES
Computer Science