Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
On the Existence of 3-Round Zero-Knowledge Protocols
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Optimal Security Proofs for PSS and Other Signature Schemes
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Towards Practical Public Key Systems Secure Against Chosen Ciphertext Attacks
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
Journal of Cryptology
Group Encryption: Non-interactive Realization in the Standard Model
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient non-interactive proof systems for bilinear groups
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Structure-preserving signatures and commitments to group elements
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Optimal structure-preserving signatures in asymmetric bilinear groups
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Structure preserving CCA secure encryption and applications
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Efficient zero-knowledge arguments from two-tiered homomorphic commitments
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
On the (im)possibility of projecting property in prime-order setting
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
A group signature scheme with unbounded message-dependent opening
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
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We investigate commitment schemes whose messages, keys, commitments, and decommitments are elements of bilinear groups, and whose openings are verified by pairing product equations. Such commitments facilitate efficient zero-knowledge proofs of knowledge of a correct opening. We show two lower bounds on such schemes: a commitment cannot be shorter than the message and verifying the opening in a symmetric bilinear group setting requires evaluating at least two independent pairing product equations. We also present optimal constructions that match the lower bounds in symmetric and asymmetric bilinear group settings.