Elliptic Curve Point Multiplication

A. G. Rostovtsev; E. B. Makhovenko

Paper 2003/088 Original: eprint.iacr.org/2003/088 ↗

Elliptic Curve Point Multiplication

A. G. Rostovtsev

E. B. Makhovenko

Abstract

A method for elliptic curve point multiplication is proposed with complex multiplication by Sqrt[-2] or by (1+Sqrt[-7])/2 instead of point duplication, speeding up multiplication about 1.34 times. Higher radix makes it possible to use one point duplication instead of two and to speed up computation about 1.6 times. We employ prime group order factorization in corresponding quadratic order and integer exponent reduction modulo quadratic prime in the Euclidean imaginary quadratic ring.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
History: 2003-05-07: last updated; 2003-05-07: published
Short URL: https://ia.cr/2003/088
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2003/088,
      author = {A. G. Rostovtsev and E. B. Makhovenko},
      title = {Elliptic Curve Point Multiplication},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/088},
      year = {2003},
      url = {https://eprint.iacr.org/2003/088}
}