【作者】 李建民；

【导师】 俞惠芳；

【作者基本信息】 青海师范大学 ， 软件工程， 2018， 硕士

【摘要】 在复杂的网络坏境中,单个协议已经不能满足人们的需求,需要多个协议组合在一起使用。为了满足人们这种需求,Canetti给出了通用可复合(UC)安全框架,该框架使得多个协议的组合使用问题得到解决。在UC框架中可以将协议的各个参与方用交互式图灵机(ITM)来表示,而且这些ITM只能在多项式时间内运行。由于签密(SC)和安全多方计算(SMC)协议一直被广泛应用在各个领域,所以在UC框架下研究签密和安全多方计算协议一直是学者们关注的热点。签密能够同时实现保密性和认证性,1997年郑玉良教授设计了一个签密方案,即能够同时实现加密和签名。自签密概念提出后受到学者们的青睐,而且提出了很多签密协议。SMC是指通信两方或者多方在保护各自私有信息的条件下进行的保密多方协同计算,这个问题最初是由姚期智教授的百万富翁问题扩展而来,Goldreich等人对此做了进一步的研究。SMC研究的领域包括保密的去做科学计算问题、几何计算问题、数据挖掘问题及统计分析问题等方面的研究工作。本论文的主要研究工作包含如下几方面:(1)在UC框架下研究了自认证盲签密(self-certified blind signcryption,SCBS),SCBS协议能够同时实现盲签名和加密。SCBS协议在电子选举、电子拍卖等领域具有广泛的应用价值,由于该协议目前不具备UC安全性,迫切需要在UC框架下实现安全性。(2)在UC框架下研究了多重签密。多重签密是指两个以上参与方对同一则消息实现签名,并且要求签名结果不能因为签名者数目增多而成线性增长,该类方案在电子商务领域被广泛应用。结合自认证公钥和Meta-ElGamal多重签名协议的思想,在UC框架下设计了ElGamal型广播多重签密(ElGamal broadcasting multi-signcryption,EBMS)协议,进而在UC安全框架下分析了该协议的安全性。(3)保密的科学计算是SMC的重要部分,集合相交一直是热点问题,因为在现实生活中很多问题都可以用集合语言来描述。一般解决此类问题的方法是先用一个集合的元素来生成多项式,即集合的元素就是多项式的根,然后通过同态或秘钥共享算法进行加密,最后将其它集合中的元素依次代入到所构造的多项式中,计算出集合的势或交集。本文利用拉格朗日插值函数来构造多项式,通过判断标量乘积的值是否为零从而确定其是否为集合内的元素,然后调用IBSC协议进行保密传输。在UC框架下不仅设计了集合相交协议(set intersection,SI),而且分析了协议是否具有UC安全性。更多还原

【Abstract】 In a complex network environment,a single protocol cannot cate for people’s needs and multiple protocols are used together.In order to meet people’s needs,Canetti presented a universally composable(UC)security framework that enables the combined use of multiple protocols to be solved.Based on UC framework,participants of the protocol can be represented by interactive turing machines(ITM),and these ITMs can only run in polynomial time.Since signcryption(SC)and secure multi-party computation(SMC)protocols are used in various fields,research on them under the UC framework has already become a focus of attention of scholars.Signcryption can achieve both the confidentiality and authentication at the same time.Professor zheng proposed a signcryption scheme in 1997,where signature and encryption functions can be completed within a step.Since the concept of signcryption was put forward,the signcryption has been studied by a large number of scholars and many practical signcryption protocols have been proposed.SMC refers to confidential multi-party collaboration computing conducted by two or more participants under the condition of protecting their privacy information.The issue was originally extended by millionaire issue of Yao Qizhi.And Goldreich et al.further studied the problem.SMC research includes confidential research on science computation,geometric calculations,data mining and statistical analysis.The main research work of this paper includes the following aspects:(1)Based on the UC framework,self-certified blind signcryption(SCBS)is studied.The SCBS protocol can simultaneously fulfill blind signature and encryption in a step.The SCBS protocol has wide application value in the fields of electronic voting and electronic auction,and because the SCBS protocol does not currently have UC security,it is urgent to implement the SCBS protocol security under the UC framework.(2)Multi-signcryption is studied based on the UC framework.Multi-signcryption is that two or more signers implement signatures on the same message,and the length of the signature cannot be linearly increased for the increasing in the number of signers.This type of scheme is widely used in the field of e-commerce.Based on the ideas of self-certified public key and Meta-ElGamal multi-signature protocol,an ElGamal broadcast multisigncryption(EBMS)protocol is designed based on UC framework.And then the security of the protocol is analyzed under the UC security framework.Meanwhile,the UC security of the EBMS protocol is also proved.(3)Confidential science computation is an important part of SMC,and research on set interaction has always been a hot issue because many problems in real life are described in a collection language.The general solution to this problem is to use a set of elements to generate a polynomial.In other words,the elements of the set are the roots of the polynomial;and then encryption is made using homomorphic or secret key sharing algorithm;finally,the elements in other sets are put into the constructed polynomial;and the cardinality or intersection of the set is calculated.In this paper,a polynomial is constructed by using a Lagrange interpolation function.By determining whether the value of the scalar product is zero or not,it is determined whether it is an element in the set,and then the IBSC protocol is called for privacy transmission.Based on the UC framework,the set intersection protocol is designed and analyze whether the protocol is secure.更多还原