Computational Semantics for Basic Protocol Logic – A Stochastic Approach

Abstract. This paper is concerned about relating formal and computational models of cryptography in case of active adversaries when formal security analysis is done with first order logic. We first argue that the way Datta et al. defined computational semantics to their Protocol Composition Logic gives rise to problems because of focusing on occurrences of bit-strings on individual traces instead of occurrences of probability distributions of bit-strings across the distribution of traces. We therefore introduce a new, fully probabilistic method to assign computational semantics to the syntax. We present this via considering a simple example of such a formal model, the Basic Protocol Logic by K. Hasebe and M. Okada [19] , but the technique is suitable for extensions to more complex situations such as PCL. The idea is to make use of the usual mathematical treatment of stochastic processes, hence be able to treat arbitrary probability distributions, non-negligible probability of collision, causal dependence or independence, and so on. Along the way, we also point out some instances of the original syntax that had to be modified, as – although sound for formal semantics – they were not sound for computational semantics