Digital Signatures From Bilinear Pairings With Applications To Blockchains

As a novel cryptographic primitive derived from digital signature,adaptor signature has attracted much attention of cryptography researchers due to its important applications in some protocols applied to blockchains.Adaptor signature allows users to create a pre-signature with a statement of a hard relation.A pre-signature can be transformed into a valid full signature by the witness of the hard relation.The witness can be extracted through a pre-signature and its corresponding full signature.Verifiable timed signature is another cryptographic primitive derived from digital signature,which allows the signer to decide when the signature can be revealed.In some blockchain systems,verifiable timed signatures can replace time-lock scripts.In most cases,verifiable timed signatures are more universal than time-lock scripts in applications.Verifiable timed signature schemes,therefore,have attracted much attention of researchers that delving into applied cryptography and blockchain technology.BLS,a digital signature scheme based on bilinear pairings,has the advantages of short signature size and easy implementation.In the Bitcoin community,BLS is expected to be specified as the standard signature scheme.Many cryptographers try to create an adaptor signature scheme based on BLS.However,BLS is a deterministic digital signature scheme,and Erwig et al.have proved that no adaptor signature scheme can be constructed based on the deterministic digital signature scheme.In order to solve the above problem,we introduce randomness into the BLS signature algorithm,designing a new probabilistic digital signature scheme named rBLS.We has proved the rBLS satisfies existential unforgeability against chosen message attacks.Besides,the performance evaluation for rBLS have been presented in the thesis.A new adaptor signature scheme is derived from rBLS,which is the first adaptor signature scheme based on bilinear pairings.We has proved the adaptor signature scheme satisfies existential unforgeability against chosen message attacks,pre-signature adaptability and witness extractability.Besides,we has presented the performance evaluation for this scheme and introduced its application in atomic swaps protocal.A verifiable timed signature scheme is derived from BLS.We prove that this scheme satisfies soundness and existential unforgeability against chosen message attacks.Further,the algebraic structure of the time-lock puzzle scheme used in the verifiable timed signature scheme is introduced.Also,we analyze how to set the time parameters appeared in the time-lock puzzle scheme.