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

Gustavo Banegas; Ricardo Custodio; Daniel Panario

Paper 2018/554

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 $F_{2^{m}}$ of the form $f (x) = x^{2 b + c} + x^{b + c} + x^{b} + x^{c} + 1$ . Let $m = 2 b + c$ 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 $F_{2} [x]$ 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.

Metadata

Available format(s): PDF
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; 2018-06-04: received; See all versions
Short URL: https://ia.cr/2018/554
License: 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},
      url = {https://eprint.iacr.org/2018/554}
}