New Instantiations of the CRYPTO 2017 Masking Schemes

Pierre Karpman; Daniel S.  Roche

Paper 2018/492

New Instantiations of the CRYPTO 2017 Masking Schemes

Pierre Karpman and Daniel S. Roche

Abstract

At CRYPTO 2017, Belaïd et al. presented two new private multiplication algorithms over finite fields, to be used in secure masking schemes. To date, these algorithms have the lowest known complexity in terms of bilinear multiplication and random masks respectively, both being linear in the number of shares $d + 1$ . Yet, a practical drawback of both algorithms is that their safe instantiation relies on finding matrices satisfying certain conditions. In their work, Belaïd et al. only address these up to $d = 2$ and 3 for the first and second algorithm respectively, limiting so far the practical usefulness of their constructions. In this paper, we use in turn an algebraic, heuristic, and experimental approach to find many more safe instances of Belaïd et al.'s algorithms. This results in explicit instantiations up to order over large fields, and up to over practically relevant fields such as .

Note: Added an erratum in front page

Metadata

Available format(s): PDF
Category: Implementation
Publication info: A minor revision of an IACR publication in ASIACRYPT 2018
Keywords: Masking linear algebra MDS matrices
Contact author(s): pierre karpman @ univ-grenoble-alpes fr
History: 2021-12-17: last of 2 revisions; 2018-05-23: received; See all versions
Short URL: https://ia.cr/2018/492
License: CC BY

BibTeX

@misc{cryptoeprint:2018/492,
      author = {Pierre Karpman and Daniel S.  Roche},
      title = {New Instantiations of the {CRYPTO} 2017 Masking Schemes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/492},
      year = {2018},
      url = {https://eprint.iacr.org/2018/492}
}