A scalar multiplication algorithm with recovery of the y-coordinate on the montgomery form and analysis of efficiency for elliptic curve cryptosystems

Katsuyuki Okeya, Kouichi Sakurai

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We present a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve over any non-binary 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 on the Weierstrass form), and discuss the Montgomery form versus the Weierstrass form in the performance of implementation 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 curve in constrained environments such as mobile devices and smart cards.

Original languageEnglish
Pages (from-to)84-93
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE85-A
Issue number1
Publication statusPublished - Jan 1 2002

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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