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arXiv:1907.11340 · IEEE Transactions on Quantum Engineering

High-Dimensional Semiquantum Cryptography

Hasan Iqbal, Walter O. Krawec

Published Jan 1, 2020• 30 citations
arXivHTMLPDF

Abstract

A semiquantum key distribution (SQKD) protocol allows two users, one of whom is restricted in their quantum capabilities to being nearly classical, to establish a shared secret key, secure against an all-powerful adversary. The study of such protocols helps to answer the fundamental question of “how quantum” must a protocol be to gain an advantage over classical communication. In this article, we design a new SQKD protocol using high-dimensional quantum states and conduct an information theoretic security analysis. We show that, similar to the fully quantum key distribution case, high-dimensional systems can increase the noise tolerance in the semiquantum case. Furthermore, we prove several general security results which are applicable to other (S)QKD protocols (both high-dimensional ones and standard qubit-based protocols) utilizing a two-way quantum channel.

DOI
10.1109/tqe.2020.3018133

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A semiquantum key distribution (SQKD) protocol allows two users, one of whom is restricted in their quantum capabilities to being nearly classical, to establish a shared secret key, secure against an all-powerful adversary. The study of such protocols helps to answer the fundamental question of “how quantum” must a protocol be to gain an advantage over classical communication. In this article, we design a new SQKD protocol using high-dimensional quantum states and conduct an information theoretic security analysis. We show that, similar to the fully quantum key distribution case, high-dimensional systems can increase the noise tolerance in the semiquantum case. Furthermore, we prove several general security results which are applicable to other (S)QKD protocols (both high-dimensional ones and standard qubit-based protocols) utilizing a two-way quantum channel.
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.
A semi-quantum key distribution (SQKD) protocol allows two users A and B to establish a shared secret key that is secure against an all-powerful adversary E even when one of the users (e.g., B) is semi-quantum or classical in nature while the other is fully-quantum. A mediated SQKD protocol allows two semi-quantum users to establish a key with the help of an adversarial quantum server. We introduce the concept of a multi-mediated SQKD protocol where two (or more) adversarial quantum servers are used. We construct a new protocol in this model and show how it can withstand high levels of quantum noise, though at a cost to efficiency. We perform an information theoretic security analysis and, along the way, prove a general security result applicable to arbitrary MM-SQKD protocols. Finally, a comparison is made to previous (S)QKD protocols.
In this work, we design a quantum key distribution protocol, allowing two limited semiquantum or ``classical'' users to establish a shared secret key with the help of a fully quantum server. A semiquantum user can prepare and measure qubits only in the computational basis and so must rely on this quantum server to produce qubits in alternative bases and also to perform alternative measurements. However, we assume that the server is untrusted and we prove the unconditional security of our protocol even in the worst case: when this quantum server is an all-powerful adversary. We also compute a lower bound of the key rate of our protocol, in the asymptotic scenario, as a function of the observed error rate in the channel, allowing us to compute the maximally tolerated error of our protocol. Our results show that a semiquantum protocol may hold similar security to a fully quantum one.
Quantum cryptography has attracted much attention in recent years. In most existing quantum cryptographic protocols, players usually need the full quantum power of generating, manipulating or measuring quantum states. Semiquantum cryptography was proposed to deal with the issue that some players require only partial quantum power, such as preparing or measuring quantum states in the classical basis, which simplifies the implementations of quantum cryptography. However, the efficiency of the existing semiquantum cryptographic protocols was relatively low from a practical point of view. In this paper, we devise some new semiquantum key distribution (SQKD) protocols which highly improve the efficiency of the most well-known SQKD protocols [Phys. Rev. Lett. 99, 140501 (2007) & Phys. Rev. A 79, 052312 (2009)]. By letting players select their actions asymmetrically, the efficiency of our new protocols can be made asymptotically close to 100%. Besides, one of our proposed protocols also utilizes the discarded X-SIFT bits in the original SQKD protocol, which further improves the efficiency of SQKD. We prove that the proposed SQKD protocols are completely robust against the most general attack.