Connecting and Improving Direct Sum Masking and Inner Product Masking

Direct Sum Masking (DSM) and Inner Product (IP) masking are two types of countermeasures that have been introduced as alternatives to simpler (e.g., additive) masking schemes to protect cryptographic implementations against side-channel analysis. In this paper, we first show that IP masking can be written as a particular case of DSM. We then analyze the improved security properties that these (more complex) encodings can provide over Boolean masking. For this purpose, we introduce a slight variation of the probing model, which allows us to provide a simple explanation to the “security order amplification” for such masking schemes that was put forward at CARDIS 2016. We then use our model to search for new instances of masking schemes that optimize this security order amplification. We finally discuss the relevance of this security order amplification (and its underlying assumption of linear leakages) based on an experimental case study.

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