A genetic algorithm to analyze the security of quantum cryptographic protocols

In this paper we show how a genetic algorithm may be used to analyze the security of quantum key distribution (QKD) protocols. In particular, we construct an algorithm to find the maximally tolerated noise level of a QKD protocol (the threshold after which users must abort). Extending on our previous work in this area, we describe in detail the algorithm and how it is constructed. We show how preprocessing may be considered by the algorithm to improve this tolerated bound. Finally, we evaluate it on multiple QKD protocols, comparing it to known bounds and also discovering new results. We also show how it can be used to analyze the security of complicated QKD protocols requiring the adversary to interact with the users. It may also be used to detect security flaws in protocols. Our algorithm can be a useful tool in QKD research and design.

[1]  R. Renner,et al.  An information-theoretic security proof for QKD protocols , 2005, quant-ph/0502064.

[2]  Walter O. Krawec Mediated semiquantum key distribution , 2014, 1411.6024.

[3]  Charles H. Bennett,et al.  Quantum cryptography using any two nonorthogonal states. , 1992, Physical review letters.

[4]  R. Renner,et al.  Information-theoretic security proof for quantum-key-distribution protocols , 2005, quant-ph/0502064.

[5]  Daowen Qiu,et al.  Semiquantum-key distribution using less than four quantum states , 2009 .

[6]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[7]  Walter O. Krawec An algorithm for evolving multiple quantum operators for arbitrary quantum computational problems , 2014, GECCO.

[8]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[9]  Walter O. Krawec Security proof of a semi-quantum key distribution protocol , 2014, 2015 IEEE International Symposium on Information Theory (ISIT).

[10]  V. Scarani,et al.  The security of practical quantum key distribution , 2008, 0802.4155.

[11]  Martin Lukac,et al.  Evolving quantum circuits using genetic algorithm , 2002, Proceedings 2002 NASA/DoD Conference on Evolvable Hardware.

[12]  Garrison W. Greenwood,et al.  Applying evolutionary techniques to quantum computing problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

[13]  Ryutaroh Matsumoto,et al.  Improved asymptotic key rate of the B92 protocol , 2013, 2013 IEEE International Symposium on Information Theory.

[14]  Walter O. Krawec Using evolutionary techniques to analyze the security of quantum key distribution protocols , 2014, GECCO.

[15]  Walter O. Krawec An improved asymptotic key rate bound for a mediated semi-quantum key distribution protocol , 2015, Quantum Inf. Comput..

[16]  Michel Toulouse,et al.  Automatic Quantum Computer Programming: A Genetic Programming Approach , 2006, Genetic Programming and Evolvable Machines.

[17]  W. Stinespring Positive functions on *-algebras , 1955 .

[18]  Tal Mor,et al.  Quantum Key Distribution with Classical Bob , 2007, ICQNM.

[19]  V. Scarani,et al.  Security of two quantum cryptography protocols using the same four qubit states (18 pages) , 2005, quant-ph/0505035.

[20]  Nicolas Gisin,et al.  Coherent-pulse implementations of quantum cryptography protocols resistant to photon-number-splitting attacks , 2004 .