Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System

Jithra Adikari; Vassil S.  Dimitrov; Pradeep K.  Mishra

Paper 2008/145

Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System

Jithra Adikari, Vassil S. Dimitrov, and Pradeep K. Mishra

Abstract

Multiple-point multiplication on elliptic curves is the highest computational complex operation in the elliptic curve cyptographic based digital signature schemes. We describe three algorithms for multiple-point multiplication on elliptic curves over prime and binary fields, based on the representations of two scalars, as sums of mixed powers of 2 and 3. Our approaches include sliding window mechanism and some precomputed values of points on the curve. A proof for formulae to calculate the number of double-based elements, doublings and triplings below 2^n is listed. Affine coordinates and Jacobian coordinates are considered in both prime fields and binary fields. We have achieved upto 24% of improvements in new algorithms for multiple-point multiplication.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic Curve Cryptography Double-Base Number System Multiple Point Multiplication
Contact author(s): jithra adikari @ atips ca
History: 2008-03-31: received
Short URL: https://ia.cr/2008/145
License: CC BY

BibTeX

@misc{cryptoeprint:2008/145,
      author = {Jithra Adikari and Vassil S.  Dimitrov and Pradeep K.  Mishra},
      title = {Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/145},
      year = {2008},
      url = {https://eprint.iacr.org/2008/145}
}