Paper 2015/785
Double-Speed Barrett Moduli
Rémi Géraud, Diana Maimut, and David Naccache
Abstract
Modular multiplication and modular reduction are the atomic constituents of most public-key cryptosystems. Amongst the numerous algorithms for performing these operations, a particularly elegant method was proposed by Barrett. This method builds the operation $a \bmod b$ from bit shifts, multiplications and additions in $\mathbb{Z}$. This allows building modular reduction at very marginal code or silicon costs by leveraging existing hardware or software multipliers. This paper presents a method allowing doubling the speed of Barrett’s algorithm by using specific composite moduli. This is particularly useful for lightweight devices where such an optimization can make a difference in terms of power consumption, cost and processing time. The generation of composite moduli with a predetermined portion is a well-known technique and the use of such moduli is considered, in statu scientae, as safe as using randomly generated composite moduli.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- modular multiplication
- Contact author(s)
- david naccache @ ens fr
- History
- 2015-08-07: received
- Short URL
- https://ia.cr/2015/785
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/785,
author = {Rémi Géraud and Diana Maimut and David Naccache},
title = {Double-Speed Barrett Moduli},
howpublished = {Cryptology ePrint Archive, Paper 2015/785},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/785}},
url = {https://eprint.iacr.org/2015/785}
}
