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On the Multiplicative Complexity of Boolean Functions and Bitsliced Higher-Order Masking

Dahmun Goudarzi 1, 2, 3 Matthieu Rivain 1
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
Inria de Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : Higher-order masking is a widely used countermeasure to make software implementa- tions of blockciphers achieve high security levels against side-channel attacks. Unfortunately, it often comes with a strong impact in terms of performances which may be prohibitive in some contexts. This situation has motivated the research for efficient schemes that apply higher-order masking with minimal performance overheads. The most widely used approach is based on a polynomial representation of the cipher s-box(es) allowing the application of standard higher-order masking building blocks such as the ISW scheme (Ishai-Sahai-Wagner, Crypto 2003). Recently, an alterna- tive approach has been considered which is based on a bitslicing of the s-boxes. This approach has been shown to enjoy important efficiency benefits, but it has only been applied to specific block- ciphers such as AES, PRESENT, or custom designs. In this paper, we present a generic method to find a Boolean representation of an s-box with efficient bitsliced higher-order masking. Specifi- cally, we propose a method to construct a circuit with low multiplicative complexity. Compared to previous work on this subject, our method can be applied to any s-box of common size and not necessarily to small s-boxes. We use it to derive higher-order masked s-box implementations that achieve important performance gain compared to optimized state-of-the-art implementations.
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https://hal.inria.fr/hal-01379296
Contributor : Dahmun Goudarzi <>
Submitted on : Tuesday, October 11, 2016 - 1:02:13 PM
Last modification on : Thursday, July 1, 2021 - 5:58:08 PM

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  • HAL Id : hal-01379296, version 1

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Dahmun Goudarzi, Matthieu Rivain. On the Multiplicative Complexity of Boolean Functions and Bitsliced Higher-Order Masking . CHES, 2016, Santa-Barbara, United States. ⟨hal-01379296⟩

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