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arXiv:quant-ph/9801022

Security of Quantum Key Distribution Against All Collective Attacks

Eli Biham, Michel Boyer, Gilles Brassard A, Jeroen van de Graaf, Tal Mor

Published Jan 12, 1998• 15 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/9801022

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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.
The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general attacks: no matter the adversary's attack, they cannot gain useful information about the key. A much simpler task is to prove security against collective attacks, where the adversary is assumed to behave identically and independently in each round. In this work, we provide a formal framework for general QKD protocols and show that for any protocol that can be expressed in this framework, security against general attacks reduces to security against collective attacks, which in turn reduces to a numerical computation. Our proof relies on a recently developed information-theoretic tool called generalised entropy accumulation and can handle generic prepare-and-measure protocols directly without switching to an entanglement-based version.
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.
The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general attacks: no matter the adversary's attack, they cannot gain useful information about the key. A much simpler task is to prove security against collective attacks, where the adversary is assumed to behave identically and independently in each round. In this work, we provide a formal framework for general QKD protocols and show that for any protocol that can be expressed in this framework, security against general attacks reduces to security against collective attacks, which in turn reduces to a numerical computation. Our proof relies on a recently developed information-theoretic tool called generalised entropy accumulation and can handle generic prepare-and-measure protocols directly without switching to an entanglement-based version.
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.
Evaluating the theoretical limit of the amount of information Eve can steal from a quantum key distribution protocol under given conditions is one of the most important things that need to be done in security proof. In addition to source loopholes and detection loopholes, channel attacks are considered to be the main ways of information leakage, while collective attacks are considered to be the most powerful active channel attacks. Here we deduce in detail the capability limit of Eve's collective attack in non-entangled quantum key distribution, like BB84 and measurement-device-independent protocols, and entangled quantum key distribution, like device-independent protocol, in which collective attack is composed of quantum weak measurement and quantum unambiguous state discrimination detection. The theoretical results show that collective attacks are equivalent in entangled and non-entangled quantum key distribution protocols. We also find that compared with the security proof based on entanglement purification, the security proof based on collective attack not only improves the system's tolerable bit error rate, but also improves the key rate.