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.

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Semiquantum cryptography has drawn much attention in recent years since it simplifies the implementation of quantum cryptographic protocols. In this paper, we study semiquantum secure direct communication (SQSDC). Based on single-photons, we propose a two-step SQSDC protocol with identity authentication, which can be used to prevent impersonation and the man-in-the-middle attack. Different from previous protocols based on quantum entanglement or quantum memory, our protocol removes there restrictions for simplifying its physical implementation. We prove that our two-step SQSDC protocol is completely robust. That is, any adversarial attempting to learn some information on the secure message or identity strings will inevitably induce some errors that can be detected by communicators.

We consider how to privately determine whether a private set owned by Bob is a subset of another private set owned by Alice. This problem has many applications in online collaboration. We first propose an encoding method to encode a set to a vector, which can reduce a set computation problem to a vector computation. Based on this encoding scheme and two different homomorphic encryption schemes, we present two efficient protocols for private subset problem in case where both private sets are subsets of a known universal set. These protocols are secure both in the semi‐honest model and in the malicious model. We then show how to use these protocols to privately determine whether a private number is a factor of another private number. Copyright © 2017 John Wiley & Sons, Ltd.