$GF(2^n)$ Bit-Parallel Squarer Using Generalized Polynomial Basis For a New Class of Irreducible Pentanomials

Xi Xiong; Haining Fan

Paper 2014/003

$G F (2^{n})$ Bit-Parallel Squarer Using Generalized Polynomial Basis For a New Class of Irreducible Pentanomials

Xi Xiong and Haining Fan

Abstract

We present explicit formulae and complexities of bit-parallel $G F (2^{n})$ squarers for a new class of irreducible pentanomials $x^{n} + x^{n - 1} + x^{k} + x + 1$ , where $n$ is odd and $1 < k < (n - 1) / 2$ . The squarer is based on the generalized polynomial basis of $G F (2^{n})$ . Its gate delay matches the best results, while its XOR gate complexity is $n + 1$ , which is only about 2/3 of the current best results.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Keywords: •implementation
Contact author(s): xixiong91 @ gmail com
History: 2014-01-02: received
Short URL: https://ia.cr/2014/003
License: CC BY

BibTeX

@misc{cryptoeprint:2014/003,
      author = {Xi Xiong and Haining Fan},
      title = {${GF}(2^n)$ Bit-Parallel Squarer Using Generalized Polynomial Basis For a New Class of Irreducible Pentanomials},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/003},
      year = {2014},
      url = {https://eprint.iacr.org/2014/003}
}

Paper 2014/003

GF(2n) Bit-Parallel Squarer Using Generalized Polynomial Basis For a New Class of Irreducible Pentanomials

Abstract

Metadata

$G F (2^{n})$ Bit-Parallel Squarer Using Generalized Polynomial Basis For a New Class of Irreducible Pentanomials