Paper 2008/285
Hybrid Binary-Ternary Joint Sparse Form and its Application in Elliptic Curve Cryptography
Jithra Adikari, Vassil Dimitrov, and Laurent Imbert
Abstract
Multi-exponentiation is a common and time consuming operation in public-key cryptography. Its elliptic curve counterpart, called multi-scalar multiplication is extensively used for digital signature verification. Several algorithms have been proposed to speed-up those critical computations. They are based on simultaneously recoding a set of integers in order to minimize the number of general multiplications or point additions. When signed-digit recoding techniques can be used, as in the world of elliptic curves, Joint Sparse Form (JSF) and interleaving $w$-NAF are the most efficient algorithms. In this paper, a novel recoding algorithm for a pair of integers is proposed, based on a decomposition that mixes powers of 2 and powers of 3. The so-called Hybrid Binary-Ternary Joint Sparse Form require fewer digits and is sparser than the JSF and the interleaving $w$-NAF. Its advantages are illustrated for elliptic curve double-scalar multiplication; the operation counts show a gain of up to 18\%.
Note: Major correction in the theoretical analysis
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Multi-exponentiationMulti-scalar multiplicationJoint sparse formBinary-ternary number systemElliptic curves.
- Contact author(s)
- jithra adikari @ atips ca
- History
- 2008-07-03: revised
- 2008-07-03: received
- See all versions
- Short URL
- https://ia.cr/2008/285
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2008/285,
author = {Jithra Adikari and Vassil Dimitrov and Laurent Imbert},
title = {Hybrid Binary-Ternary Joint Sparse Form and its Application in Elliptic Curve Cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/285},
year = {2008},
url = {https://eprint.iacr.org/2008/285}
}
