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中文摘要：
基于位置密码学的目标是将参与方的物理位置信息作为唯一的凭证来实现某些密码学任务，如基于位置的加密．可证安全的基于位置密钥交换协议应满足对于任意位置的证明者，在基于位置密钥交换协议后，证明者和验证者之间能够协商一个共享密钥．并且，对于任意多个共谋敌手而言，该共享密钥与随机数是不可区分的．研究了基于位置密码学中密钥交换的可证明安全问题．在通用可组合安全框架下，提出了基于位置密钥交换的可证安全模型．根据基于位置密钥交换协议的需求，设计了基于位置密钥交换的理想函数．对于任意多个共谋敌手而言，该理想函数生成的共享密钥与随机数是不可区分的．同时，作为基于位置密码学的一种前提假设，设计了有界检索模型（boundedretrievalmodel，BRM）的理想函数．此外，以1一维空间的基于位置密钥交换为例，证明了该协议在BRM模型下能够实现基于位置密钥交换的理想函数．
英文摘要：
The goal of position-based cryptography is to use the geographical position of a party as its only credential to achieve some cryptographic tasks, such as position-based encryption. Position-based key exchange should have the property that if there is a prover at the claimed position, then at the end of the protocol, the verifiers should share a uniform key with it while for any one group of colluding adversaries should look indistinguishable from a key drawn uniformly at random. The provable security of key exchange in position-based cryptography is investigated in this paper. In the universally composable framework, the provable secure model of position-based key exchange is proposed. According to the security requirements of position-based key exchange, the ideal functionality of position-based key exchange is presented. For any one group of colluding adversaries, the shared key derived from the ideal functionality is indistinguishable from a random key. At the same time, the ideal functionality of bounded retrieval model is designed as one of the set-up assumptions in position-based cryptography. In addition, the position-based key exchange protocol in 1-dimension space, as an example, can securely realize the functionality of position-based key exchange in the bounded retrieval model.
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