Two Novel Efficient Signature Schemes

The dissertation proposes two novel efficient signature schemes:Certificateless multi-proxy multi-signature scheme based on RSA problem and discrete logarithm problem(DLP)and a novel ID-based threshold ring signature scheme from Schnorr's idea.· In the certificateless multi-proxy multi-signature scheme based on the classic RSA problem and discrete logarithm problem(DLP),there is a group of original sign-ers who delegate their signing rights to another group of persons called proxy group.All original and proxy singers construct together a delegation certificate m?,which provides the unforgeability,prevention of power-abuse and non-repudiation to the sys-tem.The novel point of our scheme is that we introduce the famous RSA problem into our construction and it is also constructed without using pairings which reduces the running time significantly.So there is a good superiority in running time.The se-curity of our scheme is based on two mathematical difficult problems:RSA problem and discrete logarithm problem.We prove the proposed scheme is secure against cho-sen message attack in random oracle model,and the type ?/? adversaries are all super type ?/? adversaries.Comparing with two current multi-proxy multi-signature schemes and the pairing-freeness of our scheme,we conclude that it is more applicable in terms of computational efficiency for practical applications.· Schnorr signature scheme has some potential advantages in its efficiency and complexity.Our novel ID-based threshold ring signature scheme is constructed on Schnorr's idea also has the same advantages.Introducing of the Hash function can make the length of the messages fixed and it shortens the signature length sufficiently.One direction Hash functions also protect the system secret values secure.So the first lightening point of the scheme is the introduction of Hash function.And being as an ID-based threshold ring signature,it still has the good properties of ID-based,threshold and ring signatures like unforgeability,undeniability,verifiability and un-conditional signer ambiguity properties.It also provides the robustness:check the misbehavior of one participating signer by other participating signers.Our scheme uses only one bilinear pairing in signature and two in verification.The another advan-tage of our scheme is that the number of bilinear pairings does't increase as the size of the singing group increases,hence it reduces the communication cost significantly.Our scheme is also proven to be existentially unforgeable against adaptive chosen message and identity attacks(EUF-IBTRS-CMIA)and unconditional signer ambigu-ity under the random oracle model.Comparing with the other related current ID-based threshold ring signature schemes,we conclude that our scheme is more efficient for practical applications.