Research On Several Kinds Of Cryptographic Protocols With Universally Composable Security

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.