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arXiv:1507.08930 · Physical Review A

Practical security analysis of two-way quantum-key-distribution protocols based on nonorthogonal states

Ivan Henao, Roberto M. Serra

Published Nov 13, 2015• 18 citations
arXivHTMLPDF

Abstract

Within the broad research scenario of quantum secure communication, two-way quantum key distribution (TWQKD) is a relatively new proposal for sharing secret keys that is not yet fully explored. We analyze the security of TWQKD schemes that use qubits prepared in nonorthogonal states to transmit the key. Investigating protocols that employ an arbitrary number of bases for the channel preparation, we show, in particular, that the security of the LM05 protocol cannot be improved by the use of more than two preparation bases. We also provide an alternative proof of unconditional security for a deterministic TWQKD protocol recently proposed in Beaudry et al., Phys. Rev. A 88, 062302 (2013). In addition, we introduce a deterministic protocol named ``TWQKD six-state'' and compute an analytical lower bound (which can be tightened) for the maximum amount of information that an eavesdropper could extract in this case. An interesting advantage of our approach to the security analysis of TWQKD is the great simplicity and transparency of the derivations.

DOI
10.1103/physreva.92.052317

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Within the broad research scenario of quantum secure communication, two-way quantum key distribution (TWQKD) is a relatively new proposal for sharing secret keys that is not yet fully explored. We analyze the security of TWQKD schemes that use qubits prepared in nonorthogonal states to transmit the key. Investigating protocols that employ an arbitrary number of bases for the channel preparation, we show, in particular, that the security of the LM05 protocol cannot be improved by the use of more than two preparation bases. We also provide an alternative proof of unconditional security for a deterministic TWQKD protocol recently proposed in Beaudry et al., Phys. Rev. A 88, 062302 (2013). In addition, we introduce a deterministic protocol named ``TWQKD six-state'' and compute an analytical lower bound (which can be tightened) for the maximum amount of information that an eavesdropper could extract in this case. An interesting advantage of our approach to the security analysis of TWQKD is the great simplicity and transparency of the derivations.
Within the field of quantum cryptography, two-way direct quantum secure communication is a relatively new proposal for sharing secret information that is not fully explored yet. We propose a general model for two-way deterministic quantum key distribution, and a special mapping from integers to a uniformly distributed quantum space is introduced for qubit pad preparation. A reduced model, more practical, is also proposed by relaxing the security assumption of the qubit pad preparation. The main work of this paper focuses on the security proofs of these two models. Under collective attacks, we fully analyze the security basis of the general model, and, in a relatively simple way, we provide an analytical security proof for the reduced model in a depolarization quantum channel. Our results show exactly the analytical upper-bound of the amount of useful key that a powerful eavesdropper could extract in both models, and the security of the reduced model is not reduced. One advantage of this work is that the special mapping guarantees the random distribution property of the qubit pad in a uniformly distributed quantum space, thus guaranteeing the security of the two models, and the other advantage is the simplicity of the analytical derivations of security proofs.
Semiquantum key distribution protocols are designed to allow two parties to establish a shared secret key, secure against an all-powerful adversary, even when one of the users is restricted to measuring and preparing quantum states in one single basis. While interesting from a theoretical standpoint, these protocols have the disadvantage that a two-way quantum communication channel is necessary which generally limits their theoretical efficiency and noise tolerance. In this paper, we construct a semiquantum key distribution (SQKD) protocol which actually takes advantage of this necessary two-way channel, and, after performing an information theoretic security analysis against collective attacks, we show it is able to tolerate a channel noise level higher than any prior SQKD protocol to date. We also compare the noise tolerance of our protocol to other two-way fully quantum protocols, along with BB84 with classical advantage distillation. We also comment on some practical issues involving semiquantum key distribution (in particular, concerning the potential complexity in physical implementation of our protocol as compared with other standard QKD protocols). Finally, we develop techniques that can be applied to the security analysis of other (S)QKD protocols reliant on a two-way quantum communication channel.
In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD protocol with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four-state DQKD protocol against general attacks.
Semi-quantum key distribution protocols are designed to allow two users to establish a secure secret key when one of the two users is limited to performing certain “classical” operations. There have been several such protocols developed recently, however, due to their reliance on a two-way quantum communication channel (and thus, the attacker's opportunity to interact with the qubit twice), their security analysis is difficult and little is known concerning how secure they are compared to their fully quantum counterparts. In this paper we prove the unconditional security of a particular semi-quantum protocol and derive an expression for its key rate, in the asymptotic scenario.
Semi-quantum key distribution protocols are designed to allow two users to establish a secure secret key when one of the two users is limited to performing certain "classical" operations. There have been several such protocols developed recently, however, due to their reliance on a two-way quantum communication channel (and thus, the attacker's opportunity to interact with the qubit twice), their security analysis is difficult and little is known concerning how secure they are compared to their fully quantum counterparts. In this paper we prove the unconditional security of a particular semi-quantum protocol. We derive an expression for the key rate of this protocol, in the asymptotic scenario, as a function of the quantum channel's noise. Finally, we will show that this semi-quantum protocol can tolerate a maximal noise level comparable to certain fully quantum protocols.