## Cryptology ePrint Archive: Report 2007/156

**Computational Semantics for Basic Protocol Logic - A Stochastic Approach**

*Gergei Bana and Koji Hasebe and Mitsuhiro Okada*

**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.

**Category / Keywords: **foundations / formal methods, computational methods, soundness, first order logic, active adversaries

**Date: **received 27 Apr 2007, last revised 17 Feb 2009

**Contact author: **bana at math upenn edu

**Available format(s): **PDF | BibTeX Citation

**Note: **Added some final fixes.

**Version: **20090217:232441 (All versions of this report)

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