Batch exponentiation: a fast DLP-based signature generation strategy
CCS '96 Proceedings of the 3rd ACM conference on Computer and communications security
Signature schemes based on the strong RSA assumption
ACM Transactions on Information and System Security (TISSEC)
Improved Digital Signature Suitable for Batch Verification
IEEE Transactions on Computers
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on 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
Identification of Bad Signatures in Batches
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Security analysis of batch verification on identity-based signature schemes
ICCOMP'07 Proceedings of the 11th WSEAS International Conference on Computers
Fast batch verification of multiple signatures
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Batch verification suitable for efficiently verifying a limited number of signatures
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Improvements on an authentication scheme for vehicular sensor networks
Expert Systems with Applications: An International Journal
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Modular exponentiation in an abelian group is one of the most frequently used mathematical primitives in modern cryptography. Batch verification is an algorithm for verifying many exponentiations simultaneously. We propose two fast batch verification algorithms. The first one makes use of exponents of small weight, called sparse exponents, and is asymptotically 10 times faster than individual verification and twice as fast as previous works at the same security level. The second one can only be applied to elliptic curves defined over small finite fields. Using sparse Frobenius expansion with small integer coefficients, we give a complex exponent test which is four times faster than the previous works. For example, each exponentiation in one batch asymptotically requires nine elliptic curve additions on some elliptic curves for 2^{80} security.