Trading Inversions for Multiplications in Elliptic Curve Cryptography

Mathieu Ciet; Marc Joye; Kristin Lauter; Peter L.  Montgomery

Paper 2003/257

Trading Inversions for Multiplications in Elliptic Curve Cryptography

Mathieu Ciet, Marc Joye, Kristin Lauter, and Peter L. Montgomery

Abstract

Recently, Eisentraeger-Lauter-Montgomery proposed a method for speeding up scalar multiplication on elliptic curves. That method relies on improved formulae for evaluating S = 2P + Q from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulae save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling or quadrupling a point, and present a ternary/binary method to perform efficient scalar multiplication.

Note: minor changes throughout

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. accepted for publication in Designs, Codes, and Cryptography
Keywords: elliptic curve cryptosystem
Contact author(s): klauter @ microsoft com
History: 2005-06-17: revised; 2003-12-20: received; See all versions
Short URL: https://ia.cr/2003/257
License: CC BY

BibTeX

@misc{cryptoeprint:2003/257,
      author = {Mathieu Ciet and Marc Joye and Kristin Lauter and Peter L.  Montgomery},
      title = {Trading Inversions for Multiplications in Elliptic Curve Cryptography},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/257},
      year = {2003},
      url = {https://eprint.iacr.org/2003/257}
}