Untraceable off-line cash in wallet with observers
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Improved Digital Signature Suitable for Batch Verification
IEEE Transactions on Computers
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Provably Secure and Practical Identification Schemes and Corresponding Signature Schemes
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Mix-Networks on Permutation Networks
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Attacking and Repairing Batch Verification Schemes
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Remarks on Mix-Network Based on Permutation Networks
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Receipt-free mix-type voting scheme: a practical solution to the implementation of a voting booth
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Batch zero-knowledge proof and verification and its applications
ACM Transactions on Information and System Security (TISSEC)
Batch Verification of Short Signatures
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Information Processing Letters
A DAA scheme using batch proof and verification
TRUST'10 Proceedings of the 3rd international conference on Trust and trustworthy computing
A (corrected) DAA scheme using batch proof and verification
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
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Batch verification is a useful tool in verifying a large number of cryptographic items all at one time. It is especially effective in verifying predicates based on modular exponentiation. In some cases, however, the items can be incorrect although they pass batch verification together. Such leniency can be eliminated by checking the domain of each item in advance. With this in mind, we investigate if the strict batch verification can remain more effective than separate verification. In this paper, we estimate the efficiency of such strict batch verification in several types of groups, a prime subgroup of ZZp with special/random prime p and prime subgroups defined on elliptic curves over Fp, F2m and Fpm, which are often used in DL-based cryptographic primitives. Our analysis concludes that the efficiency differs greatly depending on the choice of the group and parameters determined by the verifying predicate. Furthermore, we even show that there are some cases where batch verification, regardless of strictness, loses its computational advantage.