Study On Batch Verification Of Digital Signatures

With more acheivements of research on digital signatures, its security become higher and higher, its length become shorter and shorter, but its verify computation doesn't reduce, even becomes more complex. So how to implement efficient signature verification is a hotspot of digital signatures. Batch verification can improve the verification process efficiently. Since the first batch verification of digital signature proposed by Naccache in 1994, batch verification has become an important offshoot of digital signature.In order to improve the efficiency of the signature verification, this paper mainly concentrates on the following aspects:1. An new batch verification method is presented. An improved exponent choosing method in batch verification is presented, then we use this new method in batch verification, and discuss the correctness and security of the verification. Using this new method one can avoid an exponential computation of 1024-bit without compromising the security or increasing the computation of the verification algorithm. Finally, we use this verification to some diffierent kinds of signature schemes, and give the batch verification of those schemes.2. The problems when signature scheme can't be verified using batch verication are well studied. We improve an hierarchical signature scheme, and analyse the correctness and security of the improved scheme, and give the batch verification of the new scheme. Without compromising the security or increase of computation, the new scheme can use the batch verification.3. The application area of batch verification is extended. The signature scheme based on attribute has great advantage in accessing control, but has disadvantage in verify computational complxity. In order to overcome this disadvantage, we apply the batch verification to the single signature, give a exact definition for the batch verification in single sinature and propose some batch verification algorithms in single signature, which improve the efficiency of the signature verification.