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A GAME THEORETIC APPROACH TO STUDY THE QUANTUM KEY DISTRIBUTION BB84 PROTOCOL

MAHBOOBEH HOUSHMAND

Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran, Iran

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MONIREH HOUSHMAND

Department of Electrical Engineering, Imam Reza University, Mashhad, Iran

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HABIB RAJABI MASHHADI

Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

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https://doi.org/10.1142/S0219749911007873Cited by:0 (Source: Crossref)

Abstract

Quantum cryptography uses quantum mechanics to guarantee secure communication. BB84 is a widely used quantum key distribution that provides a way for two parties, a sender, Alice, and a receiver, Bob, to share an unconditionally secure key in the presence of an eavesdropper, Eve.

Three different criteria can be assumed to study the BB84 protocol. They are the efficiency of the protocol, the probability that Eve remains undetected, and the amount of knowledge Eve has about Alice's bit sequence.

In a previous approach, we only considered the probability that Eve remains undetected. We viewed this protocol as a three player static game in which Alice and Bob were two cooperative players and Eve was a competitive one. In our game model, Alice's and Bob's objective was to maximize the probability of detecting Eve, while Eve's objective was to minimize this probability. In this paper, our previous effort is extended and we also consider the other two criteria, i.e. the efficiency of the protocol and the amount of knowledge Eve has about Alice's bit sequence. Using these models, we show how game theory can be used to find the strategies for Alice, Bob and Eve.

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