Redundant Trinomials for Finite Fields of Characteristic $2$

Christophe Doche

Paper 2004/055

Redundant Trinomials for Finite Fields of Characteristic $2$

Christophe Doche

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 when no irreducible trinomial of degree exists. Tests with {\tt NTL} show that improvements for squaring and exponentiation are respectively up to \% and \%. 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 \%.

Metadata

Available format(s): PDF PS
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: finite field arithmetic elliptic curve cryptography
Contact author(s): doche @ ics mq edu au
History: 2004-03-05: revised; 2004-02-23: received; See all versions
Short URL: https://ia.cr/2004/055
License: CC BY

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}
}

Paper 2004/055

Redundant Trinomials for Finite Fields of Characteristic 2

Abstract

Metadata

Redundant Trinomials for Finite Fields of Characteristic $2$