Orthogonal Direct Sum Masking

Abstract : Secure elements, such as smartcards or trusted platform modules (TPMs), must be protected against implementation-level attacks. Those include side-channel and fault injection attacks. We introduce ODSM, Orthogonal Direct Sum Masking, a new computation paradigm that achieves protection against those two kinds of attacks. A large vector space is structured as two supplementary orthogonal subspaces. One subspace (called a code $\mathcal{C}$) is used for the functional computation, while the second subspace carries random numbers. As the random numbers are entangled with the sensitive data, ODSM ensures a protection against (monovariate) side-channel attacks. The random numbers can be checked either occasionally, or globally, thereby ensuring a detection capability. The security level can be formally detailed: it is proved that monovariate side-channel attacks of order up to $d_\mathcal{C}-1$, where $d_\mathcal{C}$ is the minimal distance of $\mathcal{C}$, are impossible, and that any fault of Hamming weight strictly less than $d_\mathcal{C}$ is detected. A complete instantiation of ODSM is given for AES. In this case, all monovariate side-channel attacks of order strictly less than 5 are impossible, and all fault injections perturbing strictly less than 5 bits are detected.
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Julien Bringer, Claude Carlet, Hervé Chabanne, Sylvain Guilley, Houssem Maghrebi. Orthogonal Direct Sum Masking. 8th IFIP International Workshop on Information Security Theory and Practice (WISTP), Jun 2014, Heraklion, Crete, Greece. pp.40-56, ⟨10.1007/978-3-662-43826-8_4⟩. ⟨hal-01400919⟩

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