Modeling and analysis of quantum cryptographic protocols

Date

2008-08-29T21:13:22Z

Authors

Ware, Christopher J

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Abstract

In this thesis we develop a methodology for the modeling and analysis of quantum security protocols, and apply it to a cheat sensitive quantum bit commitment protocol. Our method consists of a formalization of the protocol in the process algebra CQP, a conversion to the PRISM modeling language, verification of security properties, and the quantitative analysis of optimal cheat strategies for a dishonest party. We also define additional syntax and operational semantics for CQP to add decision making capability. For a two party protocol involving Alice committing a bit to Bob, we show that the protocol favors a dishonest Alice over a dishonest Bob. When only one party is dishonest, and uses an optimal cheat strategy, we also show that the probability of cheat detection is bounded at 0.037 for Bob and 0.076 for Alice. In addition, a dishonest Alice is able to reveal an arbitrary commit bit with probability 1 while a dishonest Bob is only able to extract the correct bit before it is revealed with probability 0.854. This bias is interesting as it gives us insight into how the overall protocol functions and where its weaknesses are. By identifying these weaknesses we provide a foundation for future improvements to the protocol to reduce cheating bias or increase cheat detection. Finally, our methodology reveals the weakness of PRISM in modeling quantum variables to their full power and as a result we propose the development of a new modeling tool for quantum protocols.

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Keywords

Quantum Computing, Bit Commitment, Cryptography, Protocols, Verification, Cheat Sensitive, PRISM, CQP

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