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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