Study On EIGamal-type Digital Signature Schemes And Their Applications

This dissertation mainly discusses the security relations between ElGamal-type digital signatures based on discrete logarithm problem and their applications, the main results obtained are as follows: (1) Probability transformation, a new extended concept for strong equivalence proposed by Nyberg etc. is given. It is a basic tool to analysis the security relation among ElGamal -type schemes. (2) Some classifications on the security among generalized ElGamal schemes are given with probability transformation, thus some better schemes in performance may be selected very easily. (3) The security relation between ElGamal scheme and the corresponded MR(P)-type scheme is given: (4) A digital signature scheme with an inequation verification is proposed: (5) An unnecessary parameter in Nyberg-Ruppel authentic message encrypt scheme is pointed out; (6) A modified Pinch scheme is proposed which may check many cheater very easily; (7) Some advanced technology about secret sharing is formalized. So that thresh signature schemes may be constructed very easily; (8) A convertible undeniable signature scheme with perfectly zero-knowledge feature is proposed. (9) Two signature schemes recently proposed by Z.Shao are broken successfully. (10) A modified He-Klesler scheme which can withstand Tiersma attack is proposed.