arXiv:quant-ph/9605010

Bounds on Information and the Security of Quantum Cryptography

E. Biahm, Tal Mor

Published May 13, 1996• 0 citations

Abstract

Strong attacks against quantum key distribution use quantum memories and quantum gates to attack directly the final key. In this paper we extend a novel security result recently obtained, to demonstrate proofs of security against a wide class of such attacks. To reach this goal we calculate information-dependent reduced density matrices, we study the geometry of quantum mixed states, and we find bounds on the information leaked to an eavesdropper. Our result suggests that quantum cryptography is ultimately secure.

DOI: 10.48550/arxiv.quant-ph/9605010

Related papers

Bounds on Information and the Security of Quantum Cryptography

Eli Biham, Tal Mor

In this paper we use properties of quantum mixed states to find bounds on various measures of their distinguishability. These bounds are used for analyzing strong joint attacks against quantum key distribution which use quantum probes, quantum memories, and quantum gates to attack directly the final key. We present a wide class of joint attacks, and we prove security against them.

Physical Review LettersNov 17, 199775 citations

Security of Quantum Cryptography against Collective Attacks

Eli Biham, Tal Mor

We present strong attacks against quantum key distribution schemes which use quantum memories and quantum gates to attack directly the final key. We analyze a specific attack of this type, for which we find the density matrices available to the eavesdropper and the optimal information which can be extracted from them. We prove security against this attack and discuss security against any attack allowed by the rules of quantum mechanics.

arXiv:quant-ph/9605007Physical Review LettersMar 17, 1997131 citations

Quantum memory in quantum cryptography

Tal Mor

[Shortened abstract:] This thesis investigates the importance of quantum memory in quantum cryptography, concentrating on quantum key distribution schemes. In the hands of an eavesdropper -- a quantum memory is a powerful tool, putting in question the security of quantum cryptography; Classical privacy amplification techniques, used to prove security against less powerful eavesdroppers, might not be effective when the eavesdropper can keep quantum states for a long time. In this work we suggest a possible direction for approaching this problem. We define strong attacks of this type, and show security against them, suggesting that quantum cryptography is secure. We start with a complete analysis regarding the information about a parity bit (since parity bits are used for privacy amplification). We use the results regarding the information on parity bits to prove security against very strong eavesdropping attacks, which uses quantum memories and all classical data (including error correction codes) to attack the final key directly. In the hands of the legitimate users, a quantum memory is also a useful tool. We suggest a new type of quantum key distribution scheme where quantum memories are used instead of quantum channels. This scheme is especially adequate for networks of many users. The use of quantum memory also allows reducing the error rate to improve large scale quantum cryptography, and to enable the legitimate users to work with reasonable error rate.

arXiv:quant-ph/9906073Jun 21, 19997 citations

Practical security of quantum cryptography

Lars Lydersen

The peculiar properties of quantum mechanics enable possibilities not allowed by classical physics. In particular, two parties can generate a random, secret key at a distance, even though an eavesdropper can do anything permitted by the laws of physics. Measuring the quantum properties of the signals generating the key, would ultimately change them, and thus reveal the eavesdropper’s presence. This exchange of a random, secret key is known as quantum cryptography.\n\nQuantum cryptography can be, and has been proven unconditionally secure using perfect devices. However, when quantum cryptography is implemented, one must use components available with current technology. These are usually imperfect. Although the security of quantum cryptography has been proven for components with certain imperfections, the question remains: can quantum cryptography be implemented in a provable, unconditionally secure way, using components available with current technology? This thesis contains both a theoretical, and an experimental contribution to the answer of this question. On the experimental side, components used in, and complete quantum cryptography systems have been carefully examined for security loopholes. In particular, it turned out that two commercial quantum cryptography systems contained loopholes, which would allow an eavesdropper to capture the full secret key, without exposing her presence. Furthermore, this detector control attack could be implemented with current technology. The attack is applicable against a variety of quantum cryptography implementations and protocols.\n\nThe theoretical contribution consists of security proofs for quantum cryptography in a very general setting. Precisely, the security is proven with arbitrary individual imperfections in the source and detectors. These proofs should make it possible to use a wide array of imperfect devices in implementations of quantum cryptography.\n\nFinally, a secure detection scheme is proposed, immune to the detector control attack and compatible with those security proofs. Therefore, if this scheme is implemented correctly, it offers provable security.

Jan 1, 20114 citations

Security aspects of practical quantum cryptography

Gilles Brassard A, Norbert Lütkenhaus, Tal Mor +1 more

Summary form only given. Quantum information theory suggests the possibility of accomplishing tasks that are beyond the capability of classical computer science, such as information-secure cryptographic key distribution. The lack of security proofs for standard (secret- and public-) key distribution schemes, and the insecurity of the most widely used classical schemes (such as RSA and PGP) against "quantum attacks" emphasises the need for information-secure key distribution. We provide a thorough investigation of security issues for practical quantum key distribution, taking into account channel losses, and a realistic detection process.

Conference on Lasers and Electro-OpticsAug 29, 200515 citations

Assumptions in Quantum Cryptography

Normand J. Beaudry

Quantum cryptography uses techniques and ideas from physics and computer science. The combination of these ideas makes the security proofs of quantum cryptography a complicated task. To prove that a quantum-cryptography protocol is secure, assumptions are made about the protocol and its devices. If these assumptions are not justified in an implementation then an eavesdropper may break the security of the protocol. Therefore, security is crucially dependent on which assumptions are made and how justified the assumptions are in an implementation of the protocol. This thesis is primarily a review that analyzes and clarifies the connection between the security proofs of quantum-cryptography protocols and their experimental implementations. In particular, we focus on quantum key distribution: the task of distributing a secret random key between two parties. We provide a comprehensive introduction to several concepts: quantum mechanics using the density operator formalism, quantum cryptography, and quantum key distribution. We define security for quantum key distribution and outline several mathematical techniques that can either be used to prove security or simplify security proofs. In addition, we analyze the assumptions made in quantum cryptography and how they may or may not be justified in implementations. Along with the review, we propose a framework that decomposes quantum-key-distribution protocols and their assumptions into several classes. Protocol classes can be used to clarify which proof techniques apply to which kinds of protocols. Assumption classes can be used to specify which assumptions are justified in implementations and which could be exploited by an eavesdropper. Two contributions of the author are discussed: the security proofs of two two-way quantum-key-distribution protocols and an intuitive proof of the data-processing inequality.

arXiv:1505.02792Jan 1, 20147 citations