Cryptology ePrint Archive: Report 2016/831

Reducing the Number of Non-linear Multiplications in Masking Schemes

Jürgen Pulkus and Srinivas Vivek

Abstract: In recent years, methods to securely mask S-boxes against side-channel attacks by representing them as polynomials over finite binary fields have become quite efficient. A good cost model for this is to count how many non-linear multiplications are needed. In this work we improve on the current state-of-the-art generic method published by Coron-Roy-Vivek at CHES 2014 by working over slightly larger fields than strictly needed. This leads us, for example, to evaluate DES S-boxes with only 3 non-linear multiplications and, as a result, obtain \(25\%\) improvement in the running time for secure software implementations of DES when using three or more shares.

On the theoretical side, we prove a logarithmic upper bound on the number of non-linear multiplications required to evaluate any \(d\)-bit S-box, when ignoring the cost of working in unreasonably large fields. This upper bound is lower than the previous lower bounds proved under the assumption of working over the field \(\mathbb{F}_{2^d}\), and we show this bound to be sharp. We also achieve a way to evaluate the AES S-box using only 3 non-linear multiplications over \(\mathbb{F}_{2^{16}}\).

Category / Keywords: implementation / side-channel countermeasure, masking, probing security, block cipher, software implementation, polynomial evaluation

Original Publication (in the same form): IACR-CHES-2016
DOI:
10.1007/978-3-662-53140-2_23

Date: received 27 Aug 2016

Contact author: Juergen Pulkus at gi-de com; sv venkatesh@bristol ac uk

Available format(s): PDF | BibTeX Citation

Note: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Springer at http://link.springer.com/chapter/10.1007%2F978-3-662-53140-2_23. Please refer to any applicable terms of use of the publisher.

Version: 20160830:212630 (All versions of this report)

Short URL: ia.cr/2016/831

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