Some New Results on Binary Polynomial Multiplication

Murat Cenk; M.  Anwar Hasan

Paper 2015/094

Some New Results on Binary Polynomial Multiplication

Murat Cenk and M. Anwar Hasan

Abstract

This paper presents several methods for reducing the number of bit operations for multiplication of polynomials over the binary field. First, a modified Bernstein’s 3-way algorithm is introduced, followed by a new 5-way algorithm. Next, a new 3-way algorithm that improves asymptotic arithmetic complexity compared to Bernstein’s 3-way algorithm is introduced. This new algorithm uses three multiplications of one-third size polynomials over the binary field and one multiplication of one-third size polynomials over the finite field with four elements. Unlike Bernstein’s algorithm, which has a linear delay complexity with respect to input size, the delay complexity of the new algorithm is logarithmic. The number of bit operations for the multiplication of polynomials over the finite field with four elements is also computed. Finally, all these new results are combined to obtain improved complexities.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Keywords: Polynomial multiplication binary fields
Contact author(s): mcenk @ metu edu tr
History: 2015-02-23: received
Short URL: https://ia.cr/2015/094
License: CC BY

BibTeX

@misc{cryptoeprint:2015/094,
      author = {Murat Cenk and M.  Anwar Hasan},
      title = {Some New Results on Binary Polynomial Multiplication},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/094},
      year = {2015},
      url = {https://eprint.iacr.org/2015/094}
}