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On {M}ontgomery-like representations for elliptic curves over {$GF(2^k)$}

Martijn Stam, On {M}ontgomery-like representations for elliptic curves over {$GF(2^k)$}. Public Key Cryptography - PKC 2003, 6th International Workshop on Theory and Practice in Public Key Cryptography, Miami, FL, USA, January 6-8, 2003, Proceedings. ISBN 3-540-00324-X, pp. 240–253. January 2003. No electronic version available. External information


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 brief update of the survey by Hankerson et al. and conclude that, for non-constrained devices, using a Montgomery-representation is slower for both single and double exponentiation than projective methods with $y$-coordinate.

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