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

Authors:
Jithra Adikari
Vassil S. Dimitrov
Pradeep K. Mishra
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URL: http://eprint.iacr.org/2008/145
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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.
BibTeX
@misc{eprint-2008-17822,
  title={Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System},
  booktitle={IACR Eprint archive},
  keywords={Elliptic Curve Cryptography, Double-Base Number System, Multiple Point Multiplication},
  url={http://eprint.iacr.org/2008/145},
  note={ jithra.adikari@atips.ca 13969 received 31 Mar 2008},
  author={Jithra Adikari and Vassil S. Dimitrov and Pradeep K. Mishra},
  year=2008
}