Paper 2023/406

Quasi-linear masking to protect against both SCA and FIA

Claude Carlet, Department of Mathematics, University of Paris 8 (and Paris 13 and CNRS), Saint--Denis Cedex 02, France., University of Bergen, Norway
Abderrahman Daif, BULL SAS, Les Clayes-sous-Bois, France
Sylvain Guilley, TELECOM-ParisTech, Crypto Group, Paris Cedex 13, France
Cédric Tavernier, Hensoldt France, Plaisir, France

The implementation of cryptographic algorithms must be protected against physical attacks. Side-channel and fault injection analyses are two prominent such implem\-entation-level attacks. Protections against either do exist; they are characterized by security orders: the higher the order, the more difficult the attack. In this paper, we leverage fast discrete Fourier transform to reduce the complexity of high-order masking, and extend it to allow for fault detection and/or correction. The security paradigm is that of code-based masking. Coding theory is amenable both to mix the information and masking material at a prescribed order, and to detect and/or correct errors purposely injected by an attacker. For the first time, we show that quasi-linear masking (pioneered by Goudarzi, Joux and Rivain at ASIACRYPT 2018) can be achieved alongside with cost amortisation. This technique consists in masking several symbols/bytes with the same masking material, therefore improving the efficiency of the masking. Similarly, it allows to optimize the detection capability of codes as linear codes are all the more efficient as the information to protect is longer. Namely, we prove mathematically that our scheme features side-channel security order of $d+1-t$, detects $d$ faults and corrects $\lfloor(d-1)/2\rfloor$ faults, where $2d+1$ is the encoding length and $t$ is the information size ($t\geq1$). Applied to AES, one can get side-channel protection of order $d=7$ when masking one column/line ($t=4$ bytes) at once. In addition to the theory, that makes use of the Frobenius Additive Fast Fourier Transform, we show performance results, both in software and hardware.

Available format(s)
Publication info
Side-channel analysis (SCA)Fault injection analysis (FIA)Code-Based MaskingFault DetectionCost amortization
Contact author(s)
daif abde @ yahoo fr
2023-03-24: approved
2023-03-21: received
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      author = {Claude Carlet and Abderrahman Daif and Sylvain Guilley and Cédric Tavernier},
      title = {Quasi-linear masking to protect against both SCA and FIA},
      howpublished = {Cryptology ePrint Archive, Paper 2023/406},
      year = {2023},
      note = {\url{}},
      url = {}
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