Paper 2007/156 Original: eprint.iacr.org/2007/156 ↗

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 present a criticism of the way Datta et al. defined computational semantics to their Protocol Composition Logic, concluding that problems arise from 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 of K. Hasebe and M. Okada, 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.