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Wireless security has been an active research area since the last decade. A lot of studies of wireless security use cryptographic tools, but traditional cryptographic tools are normally based on computational assumptions, which may turn out to be invalid in the future. Consequently, it is very desirable to build cryptographic tools that do not rely on computational assumptions. In this paper, we focus on a crucial cryptographic tool, namely 1-out-of-2 oblivious transfer. This tool plays a central role in cryptography because we can build a cryptographic protocol for any polynomial-time computable function using this tool. We present a novel 1-out-of-2 oblivious transfer protocol based on wireless channel characteristics, which does not rely on any computational assumption. We also illustrate the potential broad applications of this protocol by giving an application on private communications. We have fully implemented this protocol on wireless devices and conducted experiments in real environments to evaluate the protocol and its application to private communications. Our experimental results demonstrate that it has reasonable efficiency.