ON THE SECURITY OF CRYPTOGRAPHIC CIRCUITS:PROTECTION AGAINST PROBING ATTACKS AND PERFORMANCE IMPROVEMENT OF GARBLED CIRCUITS

Dealing with secure computation and communication in hardware devices, an attacker that threatens to security of the systems can be of two different types. The first type of attacker is external to the exchange of secret messages and tries to steal some sensitive information. Probing a circuit is a useful technique through which an attacker can derive information correlated with the secret manipulated by a cryptographic circuit. Probing security is the branch of research that tries to devise models, tools and countermeasures against this type of attacks. We define a new methodology that allows to determine if a gadget (i.e., a portion of a circuit) is secure against probing attacks. Moreover, we reason about composability of gadgets, in such a way that also this composition is probing secure. The reasoning is extended also to the case in which glitches are considered, namely when the attacks are mounted when timing hazards are present. The proposed methodology is based on the construction of the Walsh matrix of a Boolean function that describes the operations of the circuit. This method allows reaching an exact solution, but generally needs a lot of computation’s time (mainly for big gadgets). To overcome the problem, we propose to compute the Walsh matrix exploiting the theory and applications of Algebraic Decision Diagrams (ADDs). Different is the case when the malicious part is internal: each party is interested in protecting its own sensitive information from all the others. When the parties are only two, from literature the garbled circuit protocol is a solution that allows to reach a result implying some secrets, without sharing them. The cost of this protocol depends on the number of extit{and} gates in the circuit that implements the Boolean function describing the protocol computations. In this context, we work to reduce the number of multiplications in two classes of particular Boolean functions, called autosymmetric and D-reducible. Moreover, in the context of the garbled circuit protocol, we discuss some innovative solutions to further reduce the protocol's costs, as the application of the 3-valued logic. This logic is an extension of the Boolean one, resulting from the addition of a new element to the set Boolean set ${0,1}$.