格上的新型安全多方集合运算的研究

发布时间：2018-06-05 08:45

本文选题：密码学 + 格　；参考：《西安电子科技大学》2014年硕士论文

【摘要】：安全多方计算主要研究的是,多个参与方在不泄露自己秘密信息的情况下,如何安全的得到一个共同的目标。安全多方计算一直是近年来密码学界的一个研究热点,在电子选举、电子拍卖、门限签名等场景中发挥着重要的作用。但是大多数安全多方计算协议,都要用到复杂的对运算、复杂的模指数运算,并且不能抵抗量子攻击。而格密码由于具有渐进效率高、代数结构简单清晰、可抵抗量子攻击以及可证明安全等优点,成为解决安全多方计算问题的一个重要工具。本文主要研究了安全多方计算领域中的集合问题,包括多方集合的相等、交集与并集问题。目前关于集合问题的解决方案大多数都是针对两方的情况,对多方参与的情况研究较少；并且大多数安全多方集合运算方案使用的是基于大数分解、离散对数等困难问题的加密算法,计算过程复杂。为了解决以上问题,本文将格上的LWE问题与安全多方集合运算问题相结合,提出了半诚实模型下基于格上LWE加密的多方参与者集合问题的方案,解决了与集合相关的三个实际问题。本文的主要成果如下：1.构造了安全多方集合相等的判定方案。该方案将集合数据转化为每个参与者的私钥,然后使用LWE加密算法对随机字符串进行加解密,最后只需TTP进行解密字符串的比较,即可解决判定多个集合相等与否的问题。2.研究和分析了求解多方集合交集的问题。首先给出了元素与集合归属关系的判定协议,然后根据判定关系给出了多方参与情况下求解交集的方案,方案包括两种方法,分别是依次计算交集和选择内部第三方参与计算交集,两种方法在通信轮数和每轮的计算量方面各有不同。3.在以上求解多方交集问题方案的基础上,进一步构造了解决多方集合并集问题的方案。根据TTP对密文键值对集合的剔除和乱序处理,以及参与者的加解密操作,从而得到所有集合的并集。本文提出的三个方案能够适用于任意数量的参与者集合运算问题,使得方案的适用范围更广泛；并将各参与方的集合数据转化为私钥,省略了加密算法中私钥的选取过程；安全性建立在LWE困难性假设的基础上,使得方案具有抗密钥泄漏和抗量子攻击的特性。不足之处在于,其中两个方案引入了外部可信第三方,而可信第三方的安全性至今仍是实际应用中的瓶颈问题。
[Abstract]:The main research of secure multi-party computing is how to obtain a common goal safely without revealing their secret information. Secure multi-party computing has been a research hotspot in cryptography in recent years. It plays an important role in electronic election, electronic auction, threshold signature and other scenarios. However, most secure multiparty computing protocols use complex pair operations, complex modular exponent operations, and cannot resist quantum attacks. Lattice cryptography has the advantages of high asymptotic efficiency, simple and clear algebraic structure, resistance to quantum attack and provable security, so it becomes an important tool to solve the problem of secure multi-party computing. In this paper, we mainly study the set problems in the field of secure multi-party computing, including the equality, intersection and union of multi-party sets. At present, most of the solutions to the set problem are aimed at the situation of both parties, but there is little research on the situation of multi-party participation, and most of the secure multi-party set operation schemes are based on the decomposition of large numbers. The encryption algorithm for difficult problems such as discrete logarithm is complicated. In order to solve the above problems, this paper combines the LWE problem on lattice with the secure multi-party set operation problem, and proposes a scheme of multi-participant set problem based on LWE encryption on lattice under semi-honest model. Three practical problems related to the set are solved. The main results of this paper are as follows: 1. A decision scheme for the equality of secure multiparty sets is constructed. The scheme converts the set data into the private key of each participant, and then encrypts and decrypts random strings by using LWE encryption algorithm. Finally, the problem of determining whether multiple sets are equal or not can be solved by comparing the decrypted strings with TTP. The problem of solving the intersection of multi-party sets is studied and analyzed. In this paper, a decision protocol for the relationship between element and set is given, and then a scheme for solving the intersection in the case of multi-party participation is given according to the decision relation. The scheme includes two methods. The intersection is calculated in turn and the third party is chosen to participate in the calculation of the intersection. The two methods are different in terms of the number of communication wheels and the amount of calculation per round. On the basis of the above solutions to the multi-party intersection problem, the scheme to solve the multi-party set union problem is further constructed. According to TTP, the key and value of ciphertext are removed and scrambled, and the encrypt and decryption operations of participants are also carried out to obtain the union of all sets. The three schemes proposed in this paper can be applied to any number of participants, which makes the scheme more applicable, and converts the data of each participant into private key, thus omitting the process of selecting private key in encryption algorithm. The security is based on the assumption of LWE difficulty, which makes the scheme have the characteristics of resisting key leakage and quantum attack. The drawback is that two of the schemes introduce external trusted third parties, and the security of trusted third parties is still a bottleneck in practical applications.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.1

【相似文献】