### A new class of irreducible pentanomials for polynomial based multipliers in binary fields

Gustavo Banegas, Ricardo Custodio, and Daniel Panario

##### Abstract

We introduce a new class of irreducible pentanomials over ${\mathbb F}_{2^m}$ of the form $f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1$. Let $m=2b+c$ and use $f$ to define the finite field extension of degree $m$. We give the exact number of operations required for computing the reduction modulo $f$. We also provide a multiplier based on Karatsuba algorithm in $\mathbb{F}_2[x]$ combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.

Available format(s)
Publication info
Published elsewhere. Journal of Cryptographic Engineering
DOI
10.1007/s13389-018-0197-6
Contact author(s)
gustavo @ crytpme in
History
2018-11-10: last of 2 revisions
See all versions
Short URL
https://ia.cr/2018/554

CC BY

BibTeX

@misc{cryptoeprint:2018/554,
author = {Gustavo Banegas and Ricardo Custodio and Daniel Panario},
title = {A new class of irreducible pentanomials for polynomial based multipliers in binary fields},
howpublished = {Cryptology ePrint Archive, Paper 2018/554},
year = {2018},
doi = {10.1007/s13389-018-0197-6},
note = {\url{https://eprint.iacr.org/2018/554}},
url = {https://eprint.iacr.org/2018/554}
}

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