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arXiv:1005.4504 · International Journal of Network Security & Its Applications

Analysis of the Security of BB84 by Model Checking

Mohamed Elboukhari, Mostafa Azizi, Abdelmalek Azizi

Published Apr 12, 2010• 19 citations
arXivHTMLPDF

Abstract

Quantum Cryptography or Quantum key distribution (QKD) is a technique that allows the secure distribution of a bit string, used as key in cryptographic protocols.When it was noted that quantum computers could break public key cryptosystems based on number theory extensive studies have been undertaken on QKD.Based on quantum mechanics, QKD offers unconditionally secure communication.Now, the progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years.Efforts are made to improve the performance and reliability of the implemented technologies.But several challenges remain despite this big progress.The task of how to test the apparatuses of QKD For example did not yet receive enough attention.These devises become complex and demand a big verification effort.In this paper we are interested in an approach based on the technique of probabilistic model checking for studying quantum information.Precisely, we use the PRISM tool to analyze the security of BB84 protocol and we are focused on the specific security property of eavesdropping detection.We show that this property is affected by the parameters of quantum channel and the power of eavesdropper.

DOI
10.5121/ijnsa.2010.2207

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Quantum Cryptography or Quantum key distribution (QKD) is a technique that allows the secure distribution of a bit string, used as key in cryptographic protocols.When it was noted that quantum computers could break public key cryptosystems based on number theory extensive studies have been undertaken on QKD.Based on quantum mechanics, QKD offers unconditionally secure communication.Now, the progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years.Efforts are made to improve the performance and reliability of the implemented technologies.But several challenges remain despite this big progress.The task of how to test the apparatuses of QKD For example did not yet receive enough attention.These devises become complex and demand a big verification effort.In this paper we are interested in an approach based on the technique of probabilistic model checking for studying quantum information.Precisely, we use the PRISM tool to analyze the security of BB84 protocol and we are focused on the specific security property of eavesdropping detection.We show that this property is affected by the parameters of quantum channel and the power of eavesdropper.
Unlike classical cryptography which is based on mathematical functions, Quantum Cryptography or Quantum Key Distribution (QKD) exploits the laws of quantum physics to offer unconditionally secure communication.The progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years and efforts are made to improve the performance and reliability of the implemented technologies.But despite this big progress, several challenges remain.For example the task of how to test the devices of QKD did not yet receive enough attention.These apparatuses become heterogeneous, complex and so demand a big verification effort.In this paper we propose to study quantum cryptography protocols by applying the technique of probabilistic model checking.Using PRISM tool, we analyze the security of BB84 protocol and we are focused on the specific security property of eavesdropper's information gain on the key derived from the implementation of this protocol.We show that this property is affected by the parameters of the eavesdropper's power and the quantum channel.
Unlike classical cryptography which is based on mathematical functions, Quantum Cryptography or Quantum Key Distribution (QKD) exploits the laws of quantum physics to offer unconditionally secure communication. The progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years and efforts are made to improve the performance and reliability of the implemented technologies. But despite this big progress, several challenges remain. For example the task of how to test the devices of QKD did not yet receive enough attention. These apparatuses become heterogeneous, complex and so demand a big verification effort. In this paper we propose to study quantum cryptography protocols by applying the technique of probabilistic model checking. Using PRISM tool, we analyze the security of BB84 protocol and we are focused on the specific security property of eavesdropper's information gain on the key derived from the implementation of this protocol. We show that this property is affected by the parameters of the eavesdropper’s power and the quantum channel.
Quantum key distribution is a technique to securely distribute a bit string between two parties by using the laws of quantum mechanics. The security of this technique depends on the basis of quantum mechanics rather than the difficulty of the mathematical calculation as in the classical encoding. Researches in this field have shown that the quantum key distribution will be fully functioning outside the laboratory in a few years. Due to the complexity and the high efficiency of the device, the verification is needed. In this article, we use PRISM to verify the security of the quantum key distribution protocol, which uses the entangled photon based on BB84 protocol.
This paper discusses the use of computer-aided verification as a practical means for analysing quantum information systems; specifically, the BB84 protocol for quantum key distribution is examined using this method. This protocol has been shown to be unconditionally secure against all attacks in an information-theoretic setting, but the relevant security proof requires a thorough understanding of the formalism of quantum mechanics and is not easily adaptable to practical scenarios. Our approach is based on probabilistic model-checking; we have used the PRISM model-checker to show that, as the number of qubits transmitted in BB84 is increased, the equivocation of the eavesdropper with respect to the channel decreases exponentially. We have also shown that the probability of detecting the presence of an eavesdropper increases exponentially with the number of qubits. The results presented here are a testament to the effectiveness of the model-checking approach for systems where analytical solutions may not be possible or plausible.
The rapid progress of quantum computing demands secure communication protocols which are beyond classical cryptographic techniques. This necessity of Quantum Key Distribution (QKD) is met by providing security relying on the fundamental laws of quantum mechanics. In the work presented, the BB84 protocol is implemented using Qiskit platform provided by IBM. The performance is analyzed for both the ideal channel conditions and an intercept–resend eavesdropping scenario studying its security behavior and performance. 100% key agreement is observed with a QBER of 0% for the BB84 protocol executed under the ideal condition. When an eavesdropper is introduced, the QBER increases significantly, ranging from 16% to 38%, exceeding the acceptable security threshold of 11% and resulting in complete rejection of the generated key. Performance analysis carried out for key sizes between 100 and 1000 qubits shows that the execution time follows O(n) trend growing linearly. This simulation validates the correct operation of the BB84 protocol and demonstrates a detailed performance and security analysis of a QKD system using IBM Qiskit.
Quantum key distribution protocols use quantum information theories to guarantee the security of key exchange procedure, and model checking is a verification technique which could be used to test the security of it. In this paper, a new group quantum key distribution protocol is designed based on BB84 protocol, which is a possible solution to handle the security issue in communication between multi-users. Discrete time Markov chain and probabilistic computation tree logic are used to model the protocol procedure and verify its security properties in PRISM. Also, we provide the theoretical proof for this group protocol, which supports the model checking results from PRISM. Our study gives an insight into some of the major difficulties of quantum security protocol design and analysis.