Detecting weaknesses in cryptographic algorithms is of utmost importance for designing secure information systems. The state-of-the-art *soft analytical side-channel attack* (SASCA) uses physical leakage information to make probabilistic predictions about intermediate computations and combines these "guesses" with the known algorithmic logic to compute the posterior distribution over the key. This attack is commonly performed via loopy belief propagation, which, however, lacks guarantees in terms of convergence and inference quality. In this paper, we develop a fast and exact inference method for SASCA, denoted as ExSASCA, by leveraging knowledge compilation and tractable probabilistic circuits. When attacking the *Advanced Encryption Standard* (AES), the most widely used encryption algorithm to date, ExSASCA outperforms SASCA by more than 31% top-1 success rate absolute. By leveraging sparse belief messages, this performance is achieved with little more computational cost than SASCA, and about 3 orders of magnitude less than exact inference via exhaustive enumeration. Even with dense belief messages, ExSASCA still uses 6 times less computations than exhaustive inference.

The design of glitch-resistant higher-order masking schemes is an important challenge in cryptographic engineering. A recent work by Mooset al.(CHES 2019) showed that most published schemes (and all efficient ones) exhibit local or composability flaws at high security orders, leaving a critical gap in the literature on hardware masking. In this article, we first extend the simulatability framework of Belaïdet al.(EUROCRYPT 2016) and prove that a compositional strategy that is correct without glitches remains valid with glitches. We then use this extended framework to prove the first masked gadgets that enable trivial composition with glitches at arbitrary orders. We show that the resulting “Hardware Private Circuits” approach the implementation efficiency of previous (flawed) schemes. We finally investigate how trivial composition can serve as a basis for a tool that allows verifying full masked hardware implementations (e.g., of complete block ciphers) at any security order from their HDL code. As side products, we improve the randomness complexity of the best published refreshing gadgets, show that some S-box representations allow latency reductions and confirm practical claims based on implementation results.

We revisit the analysis and design of masked cryptographic implementations to prevent side-channel attacks. Our starting point is the (known) observation that proving the security of a higher-order masked block cipher exhaustively requires unrealistic computing power. As a result, a natural strategy is to split algorithms in smaller parts (or gadgets), with as main objectives to enable both simple composition (as initiated by Barthe et al. at CCS 2016) and efficient implementations. We argue that existing composition strategies allow either trivial composition with significant overheads or optimized composition with more analysis efforts. As a result, we first introduce a new definition of Probe Isolating Non-Interference (PINI) that allows both trivial composition and efficient implementations. We next prove general composition theorems for PINI gadgets that considerably simplify the analysis of complex masked implementations. We finally design efficient multiplication gadgets that satisfy this definition. As additional results, we exhibit a limitation of existing compositional strategies for the analysis of Multiple-Inputs / Multiple-Outputs (MIMO) gadgets, extend Barthe et al. definition of Strong Non-Interference (SNI) to deal with this context, and describe an optimization method to design efficient MIMO-SNI (sub)circuits. Our results allow proving the security of a recent masked AES implementation by Goudarzi and Rivain (EUROCRYPT 2017). From the implementation viewpoint, PINI implementations reach the level of performance of the best composable masking schemes for the AES Rijndael, and outperform them by significant factors for lightweight ciphers.