A Trace Based $GF(2^n)$ Inversion Algorithm

Haining Fan

Paper 2020/482

A Trace Based $GF(2^n)$ Inversion Algorithm

Haining Fan

Abstract

By associating Fermat's Little Theorem based $GF(2^n)$ inversion algorithms with the multiplicative Norm function, we present an additive Trace based $GF(2^n)$ inversion algorithm. For elements with Trace value 0, it needs 1 less multiplication operation than Fermat's Little Theorem based algorithms in some $GF(2^n)$s.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
Keywords: Finite field Inversion algorithm Norm Trace.
Contact author(s): fhn @ tsinghua edu cn
History: 2022-08-19: last of 2 revisions; 2020-04-28: received; See all versions
Short URL: https://ia.cr/2020/482
License: CC BY

BibTeX

@misc{cryptoeprint:2020/482,
      author = {Haining Fan},
      title = {A Trace Based ${GF}(2^n)$ Inversion Algorithm},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/482},
      year = {2020},
      url = {https://eprint.iacr.org/2020/482}
}