dc.description.abstract | Since digital signatures are largely adopted in many commercial applications, generating or verifying huge amount of them within a period of time is an important challenge for the cryptography researches and applications. Batch cryptography provides a solution for this challenge to let the signatures be generated or
verified efficiently.
Because payment schemes require verifying a large set of signatures, moreover, signature verification is not as efficient as signature generation in some schemes, the recent work focuses on the batch verification.
The previous researches for batch verification include DLP-based, RSA-based and pairing-based signature schemes, and there are several attacks on them. In this thesis, the preliminary background, some important schemes, and related attacks of batch verification are introduced.
The small exponents test for RSA signature verification is reconsidered. We propose a more efficient setup of key generation to avoid executing zero-knowledge protocol. In order to discuss the security of RSA batch verification, two approaches of attacks are classified. Moreover, two efficient tests based on regular
exponents are proposed. Then a new method using those efficient tests as building blocks for secure batch verification is proposed.
In the last part of this thesis, we review a hash-and-sign signature. It requires the outputs of the hash function to co-prime with each other. In order to remove the restriction of this scheme, we modify it and provide a sketch proof to prove that the proposed scheme is secure. | en_US |