Towards Model-Checking Quantum Security Protocols

Logics for reasoning about quantum states have been given in the literature. In this paper, we extend one such logic with temporal constructs mimicking the standard computational tree logic used to reason about classical transition systems. We investigate the model-checking problem for this temporal quantum logic and illustrate its use by reasoning about the BB84 key distribution protocol.

[1]  Samson Abramsky,et al.  A categorical semantics of quantum protocols , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[2]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic , 1981, Logic of Programs.

[3]  Amílcar Sernadas,et al.  Weakly complete axiomatization of exogenous quantum propositional logic , 2005, Inf. Comput..

[4]  Manas K. Patra,et al.  A Logic for Probability in Quantum Systems , 2003, CSL.

[5]  Gai CarSO.  A Logic for Reasoning about Probabilities * , 2004 .

[6]  John McCarthy,et al.  Recursive functions of symbolic expressions and their computation by machine, Part I , 1959, Commun. ACM.

[7]  Edmund M. Clarke,et al.  Formal Methods: State of the Art and Future Directions Working Group Members , 1996 .

[8]  Benoît Valiron,et al.  A Lambda Calculus for Quantum Computation with Classical Control , 2005, TLCA.

[9]  Rohit Chadha,et al.  Reasoning About Imperative Quantum Programs , 2006, MFPS.

[10]  S. Basu,et al.  Algorithms in real algebraic geometry , 2003 .

[11]  Catherine A. Meadows,et al.  Formal methods for cryptographic protocol analysis: emerging issues and trends , 2003, IEEE J. Sel. Areas Commun..

[12]  Rohit Chadha,et al.  Extending Classical Logic for Reasoning About Quantum Systems , 2009 .

[13]  Manas K. Patra,et al.  Knowledge in quantum systems , 2003, TARK '03.

[14]  Samson Abramsky,et al.  A categorical semantics of quantum protocols , 2004, LICS 2004.

[15]  E. Knill,et al.  Conventions for quantum pseudocode , 1996, 2211.02559.

[16]  Prakash Panangaden,et al.  Quantum weakest preconditions , 2005, Mathematical Structures in Computer Science.

[17]  Jonathan Grattage.  A functional quantum programming language , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[18]  Alexandru Baltag,et al.  LQP: the dynamic logic of quantum information , 2006, Mathematical Structures in Computer Science.

[19]  Ronald Fagin,et al.  A logic for reasoning about probabilities , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[20]  Jeff W. Sanders,et al.  Quantum Programming , 2000, MPC.