## A probabilistic polynomial-time calculus for analysis of cryptographic protocols (2001)

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Venue: | Electronic Notes in Theoretical Computer Science |

Citations: | 45 - 8 self |

### BibTeX

@INPROCEEDINGS{Mitchell01aprobabilistic,

author = {John C. Mitchell and Ajith Ramanathan and Andre Scedrov and Vanessa Teague},

title = {A probabilistic polynomial-time calculus for analysis of cryptographic protocols },

booktitle = {Electronic Notes in Theoretical Computer Science},

year = {2001},

publisher = {}

}

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### Abstract

We prove properties of a process calculus that is designed for analyzing security protocols. Our long-term goal is to develop a form of protocol analysis, consistent with standard cryptographic assumptions, that provides a language for expressing probabilistic polynomial-time protocol steps, a specification method based on a compositional form of equivalence, and a logical basis for reasoning about equivalence. The process calculus is a variant of CCS, with bounded replication and probabilistic polynomial-time expressions allowed in messages and boolean tests. To avoid inconsistency between security and nondeterminism, messages are scheduled probabilistically instead of nondeterministically. We prove that evaluation of any process expression halts in probabilistic polynomial time and define a form of asymptotic protocol equivalence that allows security properties to be expressed using observational equivalence, a standard relation from programming language theory that involves quantifying over possible environments that might interact with the protocol. We develop a form of probabilistic bisimulation and use it to establish the soundness of an equational proof system based on observational equivalences. The proof system is illustrated by a formation derivation of the assertion, well-known in cryptography, that ElGamal encryption’s semantic security is equivalent to the (computational) Decision Diffie-Hellman assumption. This example demonstrates the power of probabilistic bisimulation and equational reasoning for protocol security.

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Citation Context ...ith probabilistic bisimulation or the proof rules for our calculus. Another one based on I/O automata can be found in [7,8,57,58]. Previous literature on probabilistic process calculi includes, e.g., =-=[11, 40, 65]-=-. However, asymptotic equivalence as used in security does not appear in any of these references. There are studies of asymptotic equivalence in the context of bisimulations though, including e.g., [2... |

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Citation Context ...pressed by some basic term. One example of such a set of terms is based on a term calculus called OSLR studied in Mitchell, Mitchell, and Scedrov [51] (based in turn on work by Bellantoni and Hofmann =-=[9,37]).-=- The closed OSLR terms of type N m → N satisfy properties 1 and 2. For our purposes, we simply identify the probabilistic poly-time functions and basic terms. Thus, if f is a probabilistic poly-time... |

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Citation Context ...for protocol security. 1. Introduction There are a variety of methods used in the analysis of security protocols. The main systematic or formal approaches include specialized logics such as BAN logic =-=[13, 19, 27]-=-, special-purpose tools designed for cryptographic protocol analysis [39], and theorem proving [55, 56] and model-checking techniques using several general purpose tools [43, 46, 52, 61, 63]. Although... |

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Citation Context ...protocol analysis that is formal, yet closer in foundations to the mathematical setting of modern cryptography. The framework relies on a language for defining communicating polynomial-time processes =-=[28]. Th-=-e reason we restrict processes to probabilistic polynomial time is so that we can reason about the security of protocols by quantifying over all “adversarial” processes definable in the language. ... |