Cryptology ePrint Archive: Report 2020/692

Optimizing Inner Product Masking Scheme by A Coding Theory Approach

Wei Cheng and Sylvain Guilley and Claude Carlet and Sihem Mesnager and Jean-Luc Danger

Abstract: Masking is one of the most popular countermeasures to protect cryptographic implementations against side-channel analysis since it is provably secure and can be deployed at the algorithm level. To strengthen the original Boolean masking scheme, several works have suggested using schemes with high algebraic complexity. The Inner Product Masking (IPM) is one of those. In this paper, we propose a unified framework to quantitatively assess the side-channel security of the IPM in a coding-theoretic approach. Specifically, starting from the expression of IPM in a coded form, we use two defining parameters of the code to characterize its side-channel resistance. In order to validate the framework, we then connect it to two leakage metrics (namely signal-to-noise ratio and mutual information, from an information-theoretic aspect) and one typical attack metric (success rate, from a practical aspect) to build a firm foundation for our framework.

As an application, our results provide ultimate explanations on the observations made by Balasch et al. at EUROCRYPT'15 and at ASIACRYPT'17, Wang et al. at CARDIS'16 and Poussier et al. at CARDIS'17 regarding the parameter effects in IPM, like higher security order in bounded moment model. Furthermore, we show how to systematically choose optimal codes (in the sense of a concrete security level) to optimize IPM by using this framework. Eventually, we present a simple but effective algorithm for choosing optimal codes for IPM, which is of special interest for designers when selecting optimal parameters for IPM.

Category / Keywords: implementation / Side-Channel Analysis, Inner Product Masking, Coding Theory, Optimal Linear Code

Original Publication (with minor differences): IEEE Transactions on Information Forensics and Security

Date: received 9 Jun 2020, last revised 31 Jul 2020

Contact author: wei cheng at telecom-paris fr

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Version: 20200731:073147 (All versions of this report)

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