International audience

This paper presents MQ on my Mind (MQOM), a digital signature scheme based on the difficulty of solving multivariate systems of quadratic equations (MQ problem). MQOM has been submitted to the NIST call for additional post-quantum signature schemes. MQOM relies on the MPC-in-the-Head (MPCitH) paradigm to build a zero-knowledge proof of knowledge (ZK-PoK) for MQ which is then turned into a signature scheme through the Fiat-Shamir heuristic. The underlying MQ problem is non-structured in the sense that the system of quadratic equations defining an instance is drawn uniformly at random. This is one of the hardest and most studied problems from multivariate cryptogra-phy which hence constitutes a conservative choice to build candidate post-quantum cryptosystems. For the efficient application of the MPCitH paradigm, we design a specific MPC protocol to verify the solution of an MQ instance. Compared to other multivariate signature schemes based on non-structured MQ instances, MQOM achieves the shortest signatures (6.3-7.8 KB) while keeping very short public keys (few dozen of bytes). Other multivariate signature schemes are based on structured MQ problems (less conservative) which either have large public keys (e.g UOV) or use recently proposed variants of these MQ problems (e.g. MAYO).

This paper introduces lronMask, a new versatile verification tool for masking security. lronMask is the first to offer the verification of standard simulation-based security notions in the probing model as well as recent composition and expandability notions in the random probing model. It supports any masking gadgets with linear randomness (e.g. addition, copy and refresh gadgets) as well as quadratic gadgets (e.g. multiplication gadgets) that might include non-linear randomness (e.g. by refreshing their inputs), while providing complete verification results for both types of gadgets. We achieve this complete verifiability by introducing a new algebraic characterization for such quadratic gadgets and exhibiting a complete method to determine the sets of input shares which are necessary and sufficient to perform a perfect simulation of any set of probes. We report various benchmarks which show that lronMask is competitive with state-of-the-art verification tools in the probing model (maskVerif, scVerif, SILVEH, matverif). lronMask is also several orders of magnitude faster than VHAPS -the only previous tool verifying random probing composability and expandability- as well as SILVEH -the only previous tool providing complete verification for quadratic gadgets with nonlinear randomness. Thanks to this completeness and increased performance, we obtain better bounds for the tolerated leakage probability of state-of-the-art random probing secure compilers.

Second order Differential Power Analysis (2O-DPA) is a powerful side-channel attack that allows an attacker to bypass the widely used masking countermeasure. To thwart 2O-DPA, higher order masking may be employed but it implies a nonnegligible overhead. In this context, there is a need to know how efficient a 2O-DPA can be, in order to evaluate the resistance of an implementation that uses first order masking and, possibly, some hardware countermeasures. Different methods of mounting a practical 2O-DPA attack have been proposed in the literature. However, it is not yet clear which of these methods is the most efficient. In this paper, we give a formal description of the higher order DPA that are mounted against software implementations. We then introduce a framework in which the attack efficiencies may be compared. The attacks we focus on involve the combining of several leakage signals and the computation of correlation coefficients to discriminate the wrong key hypotheses. In the second part of this paper, we pay particular attention to 2O-DPA that involves the product combining or the absolute difference combining. We study them under the assumption that the device leaks the Hamming weight of the processed data together with an independent Gaussian noise. After showing a way to improve the product combining, we argue that in this model, the product combining is more efficient not only than absolute difference combining, but also than all the other combining techniques proposed in the literature.