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中文摘要：
隐私保护的计算几何问题是目前安全多方计算领域的一个研究热点。提出了一个费马问题的极值计算问题，费马问题已被广泛地运用在许多领域，比如军事、商业等领域。因此，在保证隐私的前提下，设计了一个基于点积协议的费马问题极值计算协议。提出的协议仅调用了6次点积协议，不仅简化了协议，而且没有使用第三方，安全性更高。给出了协议的正确性，而且对安全性和有效性都进行了详细的理论分析。分析结果标明，所提出的协议是安全的，而且协议复杂度低，也可用于解决其他一些安全多方的计算几何问题。
英文摘要：
Privacy-Preserving Computational Geometry（PPCG）is a hot research in relation to the Secure Multi-party Computation. The problem of the fermat problem’s extreme values is studied, which is a special case of PPCG and can be applied in many fields such as military and commercial fields. A novel computation protocol for the fermat problem’s ex-treme values is presented by using the technologies of Scalar Product Protocol which is used 6 times in a privacy-preserving situation. The protocol is much more simple and has more security which the third party is not used. At last, its correct-ness, security and efficiency are analyzed. The analysis shows that the proposed protocol is secure and has low complexity, and can be used to solve some other secure multi-party computation in computational geometry.
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