# 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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David Naccache; Damien Sauveron. 8th IFIP International Workshop on Information Security Theory and Practice (WISTP), Jun 2014, Heraklion, Crete, Greece. Springer, Lecture Notes in Computer Science, LNCS-8501, pp.40-56, 2014, Information Security Theory and Practice. Securing the Internet of Things. 〈10.1007/978-3-662-43826-8_4〉
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Julien Bringer, Claude Carlet, Hervé Chabanne, Sylvain Guilley, Houssem Maghrebi. Orthogonal Direct Sum Masking. David Naccache; Damien Sauveron. 8th IFIP International Workshop on Information Security Theory and Practice (WISTP), Jun 2014, Heraklion, Crete, Greece. Springer, Lecture Notes in Computer Science, LNCS-8501, pp.40-56, 2014, Information Security Theory and Practice. Securing the Internet of Things. 〈10.1007/978-3-662-43826-8_4〉. 〈hal-01400919〉

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