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

M. Stam

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

23 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 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.
Original languageEnglish
Title of host publicationPublic Key Cryptography (Proceedings PKC 2003, Miami, FL, January 6-8, 2003)
EditorsY.G. Desmedt
Place of PublicationBerlin
ISBN (Print)3-540-00324-X
Publication statusPublished - 2002

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


Dive into the research topics of 'On Montgomery-like representations for elliptic curves over GF (2^k)'. Together they form a unique fingerprint.

Cite this