Threshold Signature Scheme And The Design And Analysis Of Authentication Protocols

The research of this thesis consists of the following three parts: basic conceptsand tools, design and analysis of threshold signature schemes, design and formalanalysis of authentication protocols.In the first part - basic concepts and tools, the main researching prbolems arethe knowledge proving protocols of discrete logarithm and secret sharing schemes,and the following results are achieved: (l) one zero-knowledge proving protocolis given, which is used to prove double discrete logarithms and possesses of theproperties of completeness and soundness; (2) the publicly verifiable secret sharingscheme(PVSS), proposed by B. Schoenmakers, is generalized to the distributionenviroment, so a scheme of distributing publicly verifiable secret sharing (DPVSS)is given.In the second part - the design and analysis of threshold signature schemes,the following results are achieved: (3) two secure and efficient threshold RSAsignature schemes are given, and the security of these schemes are analyzed de-tailedly; (4) we point out the weaknesses of the two best so far threshold signatureschemes based on discrete logarithm; (5) the security flaws of a threshold unde-niable signature scheme (LWC scheme) are pointed out; (6) a secure and efficientthreshold undeniable signature scheme, based on discrete logarithm, is designedwith security analysisi (7) we give out the first threshold undeniable signaturescheme based on the RSA cryptosystem, and analyze it's security; (8) for thefirst time, we define the concept of threshold group sisnature clearly in terms ofeight security conditions; (9) the security shortcomings of four threshold groupsignature schemes are given; (10) we claim an open probIem to design a securethreshold group signature scheme.In the third part - the design and formal analysis of authetication proto-cols, the following results are achieved: (11) we summarize and refine eightimportant principles of design authentication protocols, and present a new tax-onomy of attacks against to cryptographic protocols; (12) we find six attaksagainst to three famous authentication protoco1s, and propose improvements totwo of the three protocols; (13) the four famous BAN like logics are introducedand compared by indicating their merits and shortcomings; (14) we analyze fOr-majly the two authelitication protocol8 we improved, using BAN logic and SVOlogic respeCtively.