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Connecting and Improving Direct Sum Masking and Inner Product Masking

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Smart Card Research and Advanced Applications (CARDIS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10728))

Abstract

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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Notes

  1. 1.

    Note that the inductive search allows us to find good linear codes with relatively large minimum distance rather quickly. For instance, we can easily obtain a desired [72, 8, 30] linear code by the inductive search with the code length 8n increasing by 16 gradually from 24 to 72. The gap \(\varDelta \) here is only \(-2\). This task takes less than 2 min when using the online Magma calculator, while it is almost intractable by the other two approaches even running on a powerful local Magma server.

  2. 2.

    http://www.atmel.com/tools/SAM4C-EK.aspx.

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Acknowledgements

François-Xavier Standaert is a research associate of the Belgian Fund for Scientific Research. This work has been funded in parts by the European Commission through the H2020 project 731591 (acronym REASSURE), the CHIST-ERA project SECODE and the ERC project 724725 (acronym SWORD).

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Authors and Affiliations

  1. ICTEAM/ELEN/Crypto Group, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Romain Poussier, Qian Guo & François-Xavier Standaert

  2. LAGA, CNRS, Univ. Paris VIII and Paris XIII, Paris, France

    Claude Carlet

  3. Secure-IC S.A.S, TELECOM-ParisTech, Crypto Group, Paris-Saclay University, CNRS, Paris, France

    Sylvain Guilley

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  1. Romain Poussier
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Correspondence to Romain Poussier .

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Editors and Affiliations

  1. University of Lübeck and WPI, Lübeck, Germany

    Thomas Eisenbarth

  2. Gemalto, La Ciotat, France

    Yannick Teglia

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Poussier, R., Guo, Q., Standaert, FX., Carlet, C., Guilley, S. (2018). Connecting and Improving Direct Sum Masking and Inner Product Masking. In: Eisenbarth, T., Teglia, Y. (eds) Smart Card Research and Advanced Applications. CARDIS 2017. Lecture Notes in Computer Science(), vol 10728. Springer, Cham. https://doi.org/10.1007/978-3-319-75208-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-75208-2_8

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