Cryptology ePrint Archive: Report 2021/363

Information Leakages in Code-based Masking: A Unified Quantification Approach

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

Abstract: This paper presents a unified approach to quantifying the information leakages in the most general code-based masking schemes. Specifically, by utilizing a uniform representation, we highlight first that all code-based masking schemes' side-channel resistance can be quantified by an all-in-one framework consisting of two easy-to-compute parameters (the dual distance and the number of conditioned codewords) from a coding-theoretic perspective. In particular, we use signal-to-noise ratio (SNR) and mutual information (MI) as two complementary metrics, where a closed-form expression of SNR and an approximation of MI are proposed by connecting both metrics to the two coding-theoretic parameters.

Secondly, considering the connection between Reed-Solomon code and SSS (Shamir's Secret Sharing) scheme, the SSS-based masking is viewed as a particular case of generalized code-based masking. Hence as a straightforward application, we evaluate the impact of public points on the side-channel security of SSS-based masking schemes, namely the polynomial masking, and enhance the SSS-based masking by choosing optimal public points for it. Interestingly, we show that given a specific security order, more shares in SSS-based masking leak more information on secrets in an information-theoretic sense.

Finally, our approach provides a systematic method for optimizing the side-channel resistance of every code-based masking. More precisely, this approach enables us to select optimal linear codes (parameters) for the generalized code-based masking by choosing appropriate codes according to the two coding-theoretic parameters. Summing up, we provide a best-practice guideline for the application of code-based masking to protect cryptographic implementations.

Category / Keywords: implementation / Side-channel attacks, Leakage quantification, Signal to Noise Ratio (SNR), Mutual Information (MI), Inner Product Masking (IPM), Shamir's Secret Sharing (SSS), Generalized Code-based Masking (GCM), Coding theory

Original Publication (in the same form): IACR-CHES-2021

Date: received 18 Mar 2021, last revised 15 Apr 2021

Contact author: wei cheng at telecom-paris fr, sylvain guilley at secure-ic com

Available format(s): PDF | BibTeX Citation

Version: 20210415:091109 (All versions of this report)

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