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Physical Review Letters

Bounds on Information and the Security of Quantum Cryptography

Eli Biham, Tal Mor

Published Nov 17, 1997• 75 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.79.4034

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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.
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.
A new attack on the quantum key distribution is proposed involving joint collective unambiguous measurements of reflected probe states from an intensity modulator and photon number splitting (PNS) measurements, i.e., nondestructive measurements of the number of information photons in the quantum communication channel. This attack does not change the relative statistics of photocounts of states with different numbers of photons, does not lead to errors on the receiver side, and, thereby, is not detected by any of known methods, including the modified decoy state method. The attack results only in additional losses in the communication channel, which are not “controlled” by the decoy state method. The dependence of introduced losses on the intensity of reflected probe states is estimated. The critical level of losses depends on a particular physical implementation of the quantum cryptography system, which determines the upper bound of the intensity of reflected probe states. The knowledge of this bound is fundamentally necessary to ensure the security of keys. The fact that the attack does not lead to errors on the receiver side and does not change the relative statistics of photocounts but only results in additional losses, which depend on the intensity according to the distinguishability of reflected probe states, does not mean that this attack transforms quantum cryptography systems from the type of cryptographic systems where the security of keys is guaranteed by fundamental quantum mechanical laws to the type of systems where this security is guaranteed by technical restrictions. Even in the presence of side channels of information leakage, the security of keys is still guaranteed by fundamental quantum mechanical restrictions on the distinguishability of states. A low level of distinguishability (“intensity”) of quantum states in side channels is naturally reached by technical tools.
[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.
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.
Abstract Various Trojan-horse attacks on quantum cryptography systems are systematically considered: an attack with passive detection of side radiation, an attack with active sensing, as well as joint attacks on states in the quantum channel, side and reflected radiation. It is shown that the most effective attack is an attack with the measurement of the number of photons in the reflected states and further joint measurement of information and reflected quantum states. Explicit estimates are obtained for the intensity of the reflected quantum states at which secret keys can be transmitted to a given length.