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

M Stam

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

24 Citations (Scopus)


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.
Translated title of the contributionOn {M}ontgomery-like representations for elliptic curves over {$GF(2^k)$}
Original languageEnglish
Title of host publicationPublic Key Cryptography - PKC 2003
PublisherSpringer Berlin Heidelberg
Pages240 - 253
Number of pages13
ISBN (Print)354000324X
Publication statusPublished - Jan 2003

Bibliographical note

Conference Proceedings/Title of Journal: Public Key Cryptography - PKC 2003, 6th International Workshop
on Theory and Practice in Public Key Cryptography, Miami, FL,
USA, January 6-8, 2003, Proceedings


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