High-Dimensional Semiquantum Cryptography

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.

Mediated Semi-Quantum Key Distribution with Improved Efficiency

“…Note that this protocol is not a semi-quantum one. Indeed, past reductions of semiquantum to one-way fully quantum protocols involve the reduction to a particular fully quantum QKD protocol [38,8] and this is the same in the mediated case here. The second interesting point is that users will abort if they ever observe a |− .…”

“…However, we can extend this to security against general attacks by first showing an equivalent entanglement based protocol and then using de Finetti [47] or postselection [48] techniques to promote our earlier analysis to the general case [21]. Note that this reduction to an entanglement based protocol is an additional contribution of this work as, prior to this, no reduction for M-SQKD protocols was known (only reductions for some classes of two-party SQKD protocols were constructed in [38,8], however they did not apply to mediated SQKD protocols). Such a reduction is important to proving security against general attacks using de Finetti style arguments [49].…”

“…To this end, the notion of semi-quantum cryptography was introduced in 2007 by Boyer et al, [1]. Originally only for key distribution [2,3,4,5,6,7,8], the field of semi-quantum cryptography has advanced to other applications including secure direct communication [9,10,11,12], secret sharing [13,14,15], identity verification [16,17], and private state comparison [18,19]. See [20] for a recent survey on semi-quantum research and [21,22] for general surveys on quantum cryptography.…”

“…As a second contribution, we also show how this protocol can be reduced to an entanglement-based protocol in order to promote security to general attacks. So far, reductions are only known for a certain subset of two-party SQKD protocols [38,8] but none were known for M-SQKD protocols. Our new reduction may be highly useful to other researchers of multi-user (S)QKD protocols, providing new methods to reduce their analysis to one-way entanglement based protocols for which many mathematical tools exist to help prove them secure.…”

High-Dimensional Quantum Conference Key Agreement

“…High-dimensional quantum cryptography has been shown to exhibit numerous advantages over qubit-based protocols, especially in two-party QKD [11,12,13,14,15,16,17,18,19,20,21,22]. Encouraged by this, it is worth investigating whether high-dimensional states can benefit QCKA.…”