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Journal of Modern Optics

Security of the private quantum channel

Jan Bouda, Vladimír Bužek

Published Jan 1, 2003• 3 citations
Publisher

Abstract

We extensively discuss the problem of encryption of quantum information. We present an attack on the private quantum channel which applies when partial classical description of the cipher text is known (the known-ciphertext attack) and show how to avoid this situation. The quantum analogue of the known-plaintext attack is also discussed.
DOI
10.1080/0950034021000057978

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We study in detail the problem of encryption of quantum information. We present an attack on a private quantum channel (PQC) which applies when partial classical description of a ciphertext is known (the so-called known-ciphertext attack) and we show how this situation can be avoided. The quantum analogue of the known plaintext attack is also discussed. We determine how correlations between quantum systems can be encrypted and we conclude that two PQCs on the subsystems form a PQC on the whole composite system. Finally, some applications of the PQC are suggested and a security of a noisy channel is discussed.
We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel E\cal EE and von Neumann entropy of the ciphertext state ϱ(0)\varrho^{(0)}ϱ(0). Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if exists) is optimizing the entropy. For non-ancillary single qubit PQC we have derived the optimal entropy for arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analyzed all the possible single qubit private quantum channels for arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.
Quantum-based cryptographic protocols are often said to enjoy security guaranteed by the fundamental laws of physics. However, even carefully designed quantum-based cryptographic schemes may be susceptible to subtle attacks that are outside the original design. As an example, we give attacks against a recently proposed ``secure communication using mesoscopic coherent states'', which employs mesoscopic states, rather than single-photon states. Our attacks can be used either as a known-plaintext attack or in the case where the plaintext has not been randomized. One of our attacks requires beamsplitters and the replacement of a lossy channel by a lossless one. It is successful provided that the original loss in the channel is so big that Eve can obtain 2k2^k2k copies of what Bob receives, where kkk is the length of the seed key pre-shared by Alice and Bob. In addition, substantial improvements over such an exhaustive key search attack can be made, whenever a key is reused. Furthermore, we remark that, under the same assumption of a known or non-random plaintext, Grover's exhaustive key search attack can be applied directly to "secure communication using mesoscopic coherent states", whenever the channel loss is more than 50 percent. Therefore, as far as information-theoretic security is concerned, optically amplified signals necessarily degrade the security of the proposed scheme, when the plaintext is known or non-random. Our attacks apply even if the mesoscopic scheme is used only for key generation with a subsequent use of the key for one-time-pad encryption. Studying those attacks can help us to better define the risk models and parameter spaces in which quantum-based cryptographic schemes can operate securely. Finally, we remark that our attacks do not affect standard protocols such as Bennett-Brassard BB84 protocol or Bennett B92 protocol, which rely on single-photon signals.
We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as $\ensuremath{\alpha}\ensuremath{\eta}$ and show that it is equivalent to a random cipher in which the required randomization is affected by coherent-state quantum noise. We describe the currently known security features of $\ensuremath{\alpha}\ensuremath{\eta}$ and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how $\ensuremath{\alpha}\ensuremath{\eta}$ used in conjunction with any standard stream cipher such as the Advanced Encryption Standard provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that $\ensuremath{\alpha}\ensuremath{\eta}$ is equivalent to a nonrandom stream cipher.