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arXiv:quant-ph/9605007 · Physical Review Letters

Security of Quantum Cryptography against Collective Attacks

Eli Biham, Tal Mor

Published Mar 17, 1997• 131 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.78.2256

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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.
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.
Security of quantum key distribution against sophisticated attacks is among the most important issues in quantum information theory. In this work we prove security against a very important class of attacks called collective attacks (under a compatible noise model) which use quantum memories and gates, and which are directed against the final key. Although attacks stronger than the collective attacks can exist in principle, no explicit example was found and it is conjectured that security against collective attacks implies also security against any attack.
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The theoretical Quantum Key-Distribution scheme of Bennett and Brassard (BB84) has been proven secure against very strong attacks including the collective attacks and the joint attacks. Though the latter are the most general attacks, collective attacks are much easier to analyze, yet, they are conjectured to be as informative to the eavesdropper. Thus, collective attacks are likely to be useful in the analysis of many theoretical and practical schemes that are still lacking a proof of security, including practical BB84 schemes. We show how powerful tools developed in previous works for proving security against the joint attack, are simplified when applied to the security of BB84 against collective attacks whilst providing the same bounds on leaked information and the same error threshold.