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Probabilistic Model-Checking of Quantum Protocols (Extended Abstract)

Rajagopal Nagarajan, Nickolas K. Papanikolaou

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

In the 1980s it was first realized that quantum–mechanical phenomena can be exploited directly for the manipulation, storage and transmission of information. The discovery of quantum algorithms for prime factorization [18] and unstructured search [7], which outperformed the best classical algorithms for these tasks significantly, opened up new vistas for computer science and gave an initial thrust to the emerging field of quantum computation. To implement a quantum algorithm, however, a large scale quantum computer is necessary and such a device has yet to be built. Research in quantum information, on the other hand, has shown that quantum effects can be harnessed to provide efficient and highly secure communication channels, which can be built using current technology. Entangled quantum states, superpositions and quantum measurement are among the characteristics of the subatomic world which nature puts at our disposal; these and related phenomena enable the development of novel techniques for computation and communication with no rival in classical computing and communication theory. The focus in this paper is on communication protocols involving the use of such phenomena. Quantum protocols have particularly important applications in cryptography. Several quantum protocols have been proposed for cryptographic tasks such as oblivious transfer, bit commitment and key distribution [8,13]. The BB84 protocol for quantum key distribution [2,14], which allows two users to establish a common secret key using a single quantum channel, has been shown to be unconditionally secure against all attacks [11]. Other quantum protocols include procedures for

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In the 1980s it was first realized that quantum–mechanical phenomena can be exploited directly for the manipulation, storage and transmission of information. The discovery of quantum algorithms for prime factorization [18] and unstructured search [7], which outperformed the best classical algorithms for these tasks significantly, opened up new vistas for computer science and gave an initial thrust to the emerging field of quantum computation. To implement a quantum algorithm, however, a large scale quantum computer is necessary and such a device has yet to be built. Research in quantum information, on the other hand, has shown that quantum effects can be harnessed to provide efficient and highly secure communication channels, which can be built using current technology. Entangled quantum states, superpositions and quantum measurement are among the characteristics of the subatomic world which nature puts at our disposal; these and related phenomena enable the development of novel techniques for computation and communication with no rival in classical computing and communication theory. The focus in this paper is on communication protocols involving the use of such phenomena. Quantum protocols have particularly important applications in cryptography. Several quantum protocols have been proposed for cryptographic tasks such as oblivious transfer, bit commitment and key distribution [8,13]. The BB84 protocol for quantum key distribution [2,14], which allows two users to establish a common secret key using a single quantum channel, has been shown to be unconditionally secure against all attacks [11]. Other quantum protocols include procedures for
Currently, theoretical and experimental work in the field of quantum cryptography is being carried out in many research centers around the world. Over the past two decades since the start of active research, many quantum cryptographic protocols have been proposed, a significant number of laboratory experiments have been performed on their practical implementation, important work has been done to prove the resistance of the proposed protocols to certain types of attacks, and the first commercial quantum key distribution systems have been developed. However, there are still many tasks and problems in the field of quantum cryptography, the solution of which is of great scientific and technical importance. So, in particular, such a promising direction as quantum protocols for direct secure communication requires further development, allowing, under certain conditions, to transfer secret information without encryption, both between two and between a large number of users. Currently, such protocols have been developed using two-and three-particle entangled states, but there are almost no similar protocols with entangled states of a larger number of qubits that do not require large quantum memory for their implementation and, at the same time, have a large information capacity. Therefore, the development of new quantum direct secure communication protocols with increased information capacity, the analysis of their resistance to attacks, as well as the determination of the best protocols according to the criteria of resistance and information capacity.
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.
The emergence of quantum computing has provided new paradigms for cryptography. On the one hand, it poses significant new threats to existing classically cryptographic systems, requiring the community to define new security models that capture what a quantum adversary can do. On the other hand, it gives us new tools to design cryptographic protocols, with weaker assumptions than in the classical world, or even protocols that are impossible classically. In this survey, we first give an overview of new security definitions for classical cryptography, considering quantum adversaries who can either only use local quantum computation (post-quantum security), or even send quantum messages and in particular have access to oracle in superposition (quantum security). We explore these new notions through the examples of commitments, zero-knowledge proofs, encryption, and signatures. Then, we present what is arguably the most famous application of quantum cryptography: quantum key distribution (QKD) protocols that take advantage of unique properties of quantum mechanics to provide secure communication unconditionally. We also explore cryptography beyond QKD, focusing on unclonable cryptography: a family of cryptographic functionalities, built with quantum states, and designed to be resistant to counterfeit by leveraging the “no-cloning” theorem. We examine in particular quantum money, but also the recent notions of unclonable encryption and copy-protection, including related variants. By presenting a comprehensive survey of these topics, this paper aims to provide a thorough understanding of the current landscape and future potential of quantum cryptography.
Quantum Cryptography is a novel approach to make the information and network world more secure. Unlike classical cryptography, quantum cryptography ensures the security of communication because it is based on the laws of Quantum Mechanics; a branch of physics that deals with the fundamental behavior of matter and their energies to the levels of subatomic particles. These particles and their intrinsic properties such as photon polarization and entanglement allow us to develop an unbreakable system of cryptographic information. Conventionally, the security has been primarily concerned with the secured distribution of secret key carried over an insecure channel. However, in Quantum Cryptographic systems the transmission of secret key is done using aforementioned laws of nature through a secured quantum channel highly susceptible to intrusion detection. Consequently, the Quantum Key Distribution (QKD), in conjunction with protocols such as BB84 protocol has emerged as an ultimate modern secured communication system. This article concentrates on briefly reviewing quantum cryptography, some recent developments and reports of its vulnerabilities.
Data protection and information security have been the essence of communication in today's digital era. Authentication and secrecy of secure communication are achieved using key-based cryptographic primitives; the security of which significantly relies upon the underlying computationally complex mathematics. Moreover, these existing cryptographic primitives are considered to be non-deterministic on the basis of the existing computational capabilities. However, the considerable advancements in the development of quantum computers have significantly enhanced parallel computations; thereby, posing a great threat to these existing encryption primitives. Thus, in the future, the physical manifestation of a large successful quantum computer is likely to break all the existing public-key encryption algorithms in no time. This has led to a remarkable surge of interest in propelling quantum mechanics into existence; subsequently, leading cryptographers to research various viable domains to offer quantum-resistant secure communications. Resultantly, quantum cryptography/quantum key distribution has emerged as a futuristic replacement for classical cryptography as it offers unconditionally secure communication along with the inherent detection of any unintended user. Thus, keeping in view the significance of this relatively newer domain of cryptography, this research focuses on presenting a consolidated review of the various Quantum Key Distribution (QKD) protocols. A comparative analysis of the working mechanism of the prominent QKD protocols is presented along with an overview of the various emerging trends that have been proposed to optimize the implementational efficiency of the BB84 protocol.