安全多方计算是由中国科学家、图灵奖获得者姚期智教授在1982年率先提出的，经过三十余年的发展与丰富，已是国际密码学界研究的热点之一，如今已成为密码学的一个重要分支，因此，研究安全多方计算具有重要的理论意义。本文主要针对安全多方计算中百万富翁问题，多方保密计算集合交集问题，以及多方保密计算最值问题展开研究，主要工作如下： 百万富翁问题属于安全多方计算的经典问题，目前已有的解决方案效率不理想，影响实际应用，而且，大多数方案不能区分两数是否相等这种情况，针对这些不足，本文提出一种解决百万富翁问题的新方案。首先，方案给出一种新的1-r编码方法，应用这种编码方法将保密数据进行编码，构造一个向量，使得保密数据与所构造向量是一一对应的。其次，基于此，本文把百万富翁问题转化为计算向量中两个元素的乘积问题，通过乘积结果区分两个保密数据的大小，进而解决了原问题，然后，应用ElGamal同态加密算法设计了相应的安全协议。最后，分析了新协议的正确性、安全性、复杂性以及性能，与已有相关协议比较，本文的协议不仅简单、高效，还能够更加细粒度地进行比较。 多方保密计算集合交集问题和多方保密计算最值问题，分别是保护隐私数据挖掘和统计分析中需要解决的基础问题。本文分析了这两个问题的研究现状及其解决方案的优缺点，目前大多数已有解决方案不能抵抗量子攻击，效率不理想，且采用云外包的解决方案较少，针对这些问题，本文给出解决这两个问题的新方案。首先，在方案中给出两种0-1编码方法，然后，利用编码方法并分别结合NTRU同态加密体制解决了这两个问题，设计出新协议，最后，分析了新协议的正确性、安全性、复杂性以及性能，文中设计的新协议相比已有解决方案不但可以抵抗量子攻击，而且效率更高。此外，针对多方保密计算集合交集和多方保密计算最值问题，这两个新协议是首次给出了云计算环境下抗量子攻击的解决方法。 本文针对以上三个问题提出新的解决方案，设计了相应的安全协议，而且给出基于协议的相关应用。

The secure multi-party computation was first proposed by Chinese scientist and Turing Award winner Professor Andrew Chi-Chih Yao in 1982. After more than 30 years of development and enrichment, it has become one of the hotspots in the field of international cryptography. Now it has become an important branch of the cryptography. Therefore, studying the secure multi-party computation has important theoretical significance and practical application value. This paper focuses on the Millionaires’ problem, multi-party secret computing set intersection problem, and multi-party secret computing maximum and minimum problem. The main work is as follows: The millionaires’ problem is a classic problem of the secure multi-party computation. However, so far the existing solutions are not efficient and affect the practical application. Moreover, most previous schemes do not distinguish whether the two numbers are equal. Aiming at these drawbacks, a new solution, in this paper, is proposed to solve the millionaires’ problem. The scheme first gives a new 1-r encoding method to construct a vector according to a given confidential data. The encoding guaranteed a kind of one-to-one correspondence between the confidential data and the vector. Then, Based on what mentioned above, the millionaires’ problem is transformed into the product of two elements in the vector. Thus, The initial problem was solved by calculating the product result to distinguish the size of the two confidential data. Subsequently, a secure protocol was designed to solve the Millionaires’ problem by taking advantage of the ElGamal homomorphic encryption algorithm. Finally, the correctness, security, complexity and performance of the new protocol are analyzed. compared with the existing related protocol, the protocol of this paper is not only simple and efficient, but also the compare was more fine-grained. The multi-party secure set intersection problem and the multi-party secure computing maximum and minimum problem, and the both of them are the basic problems that need to be solved in the privacy-preserving data mining and statistical analysis, respectively. The research status about these two problems and the advantages and disadvantages of many existing solutions are analyzed. most of the previous solutions cannot resist quantum attacks, the efficiency is not efficient, and the solutions using cloud outsourcing are less. Aiming at these issues above, two new solutions to solve these two problems are proposed in this paper. In the scheme, two kinds of 0-1 encoding methods are first given. Subsequently, the two problems are solved utilizing the 0-1 encoding methods and combining with NTRU homomorphic encryption, respectively, and new protocols are designed. At last, the correctness, security, complexity and performance of the new protocols are analyzed. the two protocols designed in this paper, compared with the previous schemes, are not only secure against the quantum attack but also more efficient. In addition, it is in the cloud computing environment that the new corresponding protocols are given to solve the these two problems at the first time. The new solutions are proposed aiming at the three problems mentioned above in this paper. the corresponding secure protocols are designed, and then related applications based on these protocols are given.