A probabilistic polynomial-time process calculus for the analysis of cryptographic protocols

We prove properties of a process calculus that is designed for analysing 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 speci...

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Vydáno v:Theoretical computer science Ročník 353; číslo 1; s. 118 - 164
Hlavní autoři: Mitchell, John C., Ramanathan, Ajith, Scedrov, Andre, Teague, Vanessa
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 14.03.2006
Elsevier
Témata:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Cryptography
Exact sciences and technology
General logic
Information, signal and communications theory
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Observational equivalence
Probabilistic bisimulation
Problem solving, game playing
Process Algebra
Sciences and techniques of general use
Security protocol analysis
Signal and communications theory
Telecommunications and information theory
Theoretical computing
Probabilistic bisimulation
Process Algebra
Observational equivalence
Security protocol analysis
Equivalence relation
Process algebra
Language theory
Computer theory
Security protocol
Time allowed
Step method
Specification
Probabilistic language
Encryption
Non determinism
Polynomial time
Cryptographic protocol
Soundness
Programming language
Bisimulation
Replication
Cryptography
Programming theory
ISSN:0304-3975, 1879-2294
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Shrnutí:We prove properties of a process calculus that is designed for analysing 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 all 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 El Gamal 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.
Bibliografie:ObjectType-Article-2
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2005.10.044