### Low Complexity Cubing and Cube Root Computation over $\F_{3^m}$ in Polynomial Basis

##### Abstract

We present low complexity formulae for the computation of cubing and cube root over $\F_{3^m}$ constructed using special classes of irreducible trinomials, tetranomials and pentanomials. We show that for all those special classes of polynomials, field cubing and field cube root operation have the same computational complexity when implemented in hardware or software platforms. As one of the main applications of these two field arithmetic operations lies in pairing-based cryptography, we also give in this paper a selection of irreducible polynomials that lead to low cost field cubing and field cube root computations for supersingular elliptic curves defined over $\F_{3^m}$, where $m$ is a prime number in the pairing-based cryptographic range of interest, namely, $m\in [47, 541]$.

Note: Second version

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Keywords
Finite field arithmeticcubingcube rootcharacteristic threecryptography
Contact author(s)
francisco @ cs cinvestav mx
History
2009-11-13: last of 2 revisions
See all versions
Short URL
https://ia.cr/2009/070

CC BY

BibTeX

@misc{cryptoeprint:2009/070,
author = {Omran Ahmadi and Francisco Rodríguez-Henriquez},
title = {Low Complexity Cubing and Cube Root Computation over $\F_{3^m}$ in Polynomial Basis},
howpublished = {Cryptology ePrint Archive, Paper 2009/070},
year = {2009},
note = {\url{https://eprint.iacr.org/2009/070}},
url = {https://eprint.iacr.org/2009/070}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.