Evaluation of anonymity and confidentiality protocols using theorem proving

Anonymity and confidentiality protocols constitute crucial parts in many network applications as they ensure anonymous communications between entities in a network or provide security in insecure communication channels. Evaluating the properties of these protocols is therefore of paramount importance, especially in the case of safety-critical applications. However, traditional analysis techniques, like simulation, cannot ascertain accurate analysis in this domain. We propose to overcome this limitation by conducting an information leakage analysis of anonymity and cryptographic protocols within the trusted kernel of a higher-order-logic theorem prover. For this purpose, we first introduce two novel measures of information leakage, namely the information leakage degree and the conditional information leakage degree and then present a higher-order-logic formalization of information measures and the underlying required theories of measure, probability and information. For illustration purposes, we use the proposed framework to evaluate the security properties of the one-time pad encryption system as well as the properties of an anonymity-based single MIX. We show how this formal analysis allowed us to find a counter-example for a theorem that was reported in the literature to describe the leakage properties of this single MIX.