Direct Division in Factor Rings

Patrick Fitzpatrick; Christopher Wolf

Paper 2004/353 Original: eprint.iacr.org/2004/353 ↗

Direct Division in Factor Rings

Patrick Fitzpatrick

Christopher Wolf

Abstract

Conventional techniques for division in the polynomial factor ring $\Ftm$ or the integer ring $\Zzs$ use a combination of inversion and multiplication. We present a new algorithm that computes the division directly and therefore eliminates the multiplication step. The algorithm requires $2\,{\rm degree\/}{(m)}$ (resp. $2 \log_2 n$) steps, each of which uses only shift and multiply-subtract operations.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
History: 2004-12-18: last updated; 2004-12-13: published
Short URL: https://ia.cr/2004/353
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2004/353,
      author = {Patrick Fitzpatrick and Christopher Wolf},
      title = {Direct Division in Factor Rings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/353},
      year = {2004},
      url = {https://eprint.iacr.org/2004/353}
}