Paper 2004/055 Original: eprint.iacr.org/2004/055 ↗
Redundant Trinomials for Finite Fields of Characteristic $2$
Abstract
In this paper we introduce a new way to represent elements of a finite field of characteristic $2$. We describe a new type of polynomial basis, called {\it redundant trinomial basis} and discuss how to implement it efficiently. Redundant trinomial bases are well suited to build $\mathbb{F}_{2^n}$ when no irreducible trinomial of degree $n$ exists. Tests with {\tt NTL} show that improvements for squaring and exponentiation are respectively up to $45$\% and $25$\%. More attention is given to relevant extension degrees for doing elliptic and hyperelliptic curve cryptography. For this range, a scalar multiplication can be speeded up by a factor up to $15$\%.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2004-03-05: last updated
- 2004-02-23: published
- Short URL
- https://ia.cr/2004/055
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2004/055,
author = {Christophe Doche},
title = {Redundant Trinomials for Finite Fields of Characteristic $2$},
howpublished = {Cryptology {ePrint} Archive, Paper 2004/055},
year = {2004},
url = {https://eprint.iacr.org/2004/055}
}