Quantum key distribution (QKD) protocols allow two parties to establish a shared secret key, secure against an all powerful adversary. This is a task impossible to achieve through classical communication only; indeed, to distribute a secret key through classical means requires one to assume computationally bounded adversaries. If, however, both parties are "quantum capable" then security may be attained assuming only that the adversary must obey the laws of physics. But "how quantum" must a protocol actually be to gain this advantage over classical communication? This is one of the questions semi-quantum cryptography seeks to answer.Semi-quantum communication, a model introduced in 2007 by M. Boyer, D. Kenigsberg, and T. Mor (PRL 99 140501), involves the use of fully-quantum users and semiquantum, or "classical" users. These classical users are only allowed to interact with the quantum channel in a limited, classical manner. Originally introduced to study the key-distribution problem, semi-quantum research has since expanded, and continues to grow, with new protocols, security proof methods, experimental implementations, and new cryptographic applications beyond key distribution. Research in the field of semi-quantum cryptography requires new insights into working with restricted protocols and, so, the tools and techniques derived in this field can translate to results in broader quantum information science. Furthermore, other questions such as the connection between quantum and classical processing, including how classical information processing can be used to counteract a quantum deficiency in a protocol, can shed light on important theoretical questions.This work surveys the history and current state-of-the-art in semi-quantum research. We discuss the model and several protocols offering the reader insight into how protocols are constructed in this realm. We discuss security proof methods and how classical post-processing can be used to counteract users' inability to perform certain quantum operations. Moving beyond key distribution, we survey current work in other * semi-quantum cryptographic protocols and current trends. We also survey recent work done in attempting to construct practical semi-quantum systems including recent experimental results in this field. Finally, as this is still a growing field, we highlight, throughout this survey, several open problems that we feel are important to investigate in the hopes that this will spur even more research in this topic.

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.

In this work we introduce a novel QKD protocol capable of smoothly transitioning, via user-tuneable parameter, from classical to semi-quantum in order to help understand the effect of quantum communication resources on secure key distribution. We perform an information theoretic security analysis of this protocol to determine what level of "quantumness" is sufficient to achieve security, and we discover some rather interesting properties of this protocol along the way.

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