On Montgomery-like representations for elliptic curves over GF (2^k)

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