## Cryptology ePrint Archive: Report 2018/492

New Instantiations of the CRYPTO 2017 Masking Schemes

Pierre Karpman and Daniel S. Roche

Abstract: At CRYPTO 2017, Bela\"id 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, Bela\"id 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 Bela\"id et al.'s algorithms. This results in explicit instantiations up to order $d = 6$ over large fields, and up to $d = 4$ over practically relevant fields such as $\mathbb{F}_{2^8}$.

Category / Keywords: implementation / Masking, linear algebra, MDS matrices

Original Publication (with minor differences): IACR-ASIACRYPT-2018

Date: received 22 May 2018, last revised 6 Sep 2018

Contact author: pierre karpman at univ-grenoble-alpes fr

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2018/492

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