[Resource Topic] 2004/055: Redundant Trinomials for Finite Fields of Characteristic $2$

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Redundant Trinomials for Finite Fields of Characteristic 2

Authors: Christophe Doche


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%.

ePrint: https://eprint.iacr.org/2004/055

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