Improving Modular Inversion in RNS using the Plus-Minus Method

Karim Bigou; Arnaud Tisserand

Paper 2015/193

Improving Modular Inversion in RNS using the Plus-Minus Method

Karim Bigou and Arnaud Tisserand

Abstract

The paper describes a new RNS modular inversion algorithm based on the extended Euclidean algorithm and the plus-minus trick. In our algorithm, comparisons over large RNS values are replaced by cheap computations modulo 4. Comparisons to an RNS version based on Fermat’s little theorem were carried out. The number of elementary modular operations is significantly reduced: a factor 12 to 26 for multiplications and 6 to 21 for additions. Virtex 5 FPGAs implementations show that for a similar area, our plus-minus RNS modular inversion is 6 to 10 times faster.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published by the IACR in CHES 2013
DOI: 10.1007/978-3-642-40349-1_14
Keywords: Residue Number System Modular Representation Extended Euclidean Algorithm Hardware Implementation ECC RSA
Contact author(s): karim bigou @ irisa fr
arnaud tisserand @ irisa fr
History: 2015-03-04: received
Short URL: https://ia.cr/2015/193
License: CC BY

BibTeX

@misc{cryptoeprint:2015/193,
      author = {Karim Bigou and Arnaud Tisserand},
      title = {Improving Modular Inversion in {RNS} using the Plus-Minus Method},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/193},
      year = {2015},
      doi = {10.1007/978-3-642-40349-1_14},
      url = {https://eprint.iacr.org/2015/193}
}