This paper discusses representations for computation on non-supersingular elliptic curves over binary fields, where computations are performed on the x-coordinates only. We discuss existing methods and present a new one, giving rise to a faster addition routine than previous Montgomery-representations. As a result a double exponentiation routine is described that requires 8.5 field multiplications per exponent bit, but that does not allow easy y-coordinate recovery. For comparison, we also give a briefu pdate oft he survey by Hankerson et al. and conclude that, for non-constrained devices, using a Montgomeryrepresentation is slower for both single and double exponentiation than projective methods with y-coordinate.
|Title of host publication||Public Key Cryptography (Proceedings PKC 2003, Miami, FL, January 6-8, 2003)|
|Place of Publication||Berlin|
|Publication status||Published - 2002|
|Name||Lecture Notes in Computer Science|