Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a montgomery-form elliptic curve

Katsuyuki Okeya, Kouichi Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

45 Citations (Scopus)

Abstract

We present a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery form elliptic curve over any nonbinary field. The previous algorithms for scalar multiplication on a Montgomery form do not consider how to recover the y-coordinate. So although they can be applicable to certain restricted schemes (e.g. ECDH and ECDSA-S), some schemes (e.g. ECDSA-V and MQV) require scalar multiplication with recovery of the y-coordinate. We compare our proposed scalar multiplication algorithm with the traditional scalar multiplication algorithms (including Window-methods in Weierstrass form), and discuss the Montgomery form versus the Weierstrass form in the performance of implementations with several techniques of elliptic curve cryptosystems (including ECES, ECDSA, and ECMQV). Our results clarify the advantage of the cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.

Original languageEnglish
Title of host publicationCryptographic Hardware and Embedded Systems - CHES 2001 - 3rd International Workshop, Proceedings
PublisherSpringer Verlag
Pages126-141
Number of pages16
Volume2162
ISBN (Print)3540425217
Publication statusPublished - 2001
Event3rd International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2001 - Paris, France
Duration: May 14 2001May 16 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2162
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2001
CountryFrance
CityParis
Period5/14/015/16/01

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Okeya, K., & Sakurai, K. (2001). Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a montgomery-form elliptic curve. In Cryptographic Hardware and Embedded Systems - CHES 2001 - 3rd International Workshop, Proceedings (Vol. 2162, pp. 126-141). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2162). Springer Verlag.