Fast Montgomery-like Square Root Computation over $GF(2^m)$ for All Trinomials

Yin Li; Yu Zhang

Paper 2017/064

Fast Montgomery-like Square Root Computation over $GF(2^m)$ for All Trinomials

Yin Li and Yu Zhang

Abstract

This letter is concerned with an extension of square root computation over $GF(2^m)$ defined by irreducible trinomials. We introduce a new type of Montgomery-like square root formulae, which is more efficient compared with classic square root operation. By choosing proper Montgomery factor regarding to different types of trinomials, the space and time complexities of our proposal outperform or match the best results. Furthermore, a practical application of the Montgomery-like square root in exponentiation computation is also presented.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: finite field square root
Contact author(s): yunfeiyangli @ gmail com
History: 2017-08-09: last of 2 revisions; 2017-01-31: received; See all versions
Short URL: https://ia.cr/2017/064
License: CC BY

BibTeX

@misc{cryptoeprint:2017/064,
      author = {Yin Li and Yu Zhang},
      title = {Fast Montgomery-like Square Root Computation over ${GF}(2^m)$ for All Trinomials},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/064},
      year = {2017},
      url = {https://eprint.iacr.org/2017/064}
}