Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Private Searching on Streaming Data
Journal of Cryptology
Homomorphic Encryption and Signatures from Vector Decomposition
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Discrete Applied Mathematics
Universally Composable Adaptive Oblivious Transfer
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient and secure protocols for privacy-preserving set operations
ACM Transactions on Information and System Security (TISSEC)
Randomizable Proofs and Delegatable Anonymous Credentials
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in 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
Hierarchical Predicate Encryption for Inner-Products
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Secure hybrid encryption from weakened key encapsulation
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
A non-interactive shuffle with pairing based verifiability
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Fully anonymous group signatures without random oracles
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
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
P-signatures and noninteractive anonymous credentials
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Fully secure functional encryption with general relations from the decisional linear assumption
CRYPTO'10 Proceedings of the 30th annual 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
Efficient attribute-based signatures for non-monotone predicates in the standard model
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Optimal structure-preserving signatures in asymmetric bilinear groups
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Converting pairing-based cryptosystems from composite-order groups to prime-order groups
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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
Separating short structure-preserving signatures from non-interactive assumptions
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Beyond the limitation of prime-order bilinear groups, and round optimal blind signatures
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Malleable proof systems and applications
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Group to group commitments do not shrink
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Tools for simulating features of composite order bilinear groups in the prime order setting
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Adaptively attribute-hiding (hierarchical) inner product encryption
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Ring signatures of sub-linear size without random oracles
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Comparing the pairing efficiency over composite-order and prime-order elliptic curves
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
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Projecting bilinear pairings have frequently been used for designing cryptosystems since they were first derived from composite order bilinear groups. There have been only a few studies on the (im)possibility of projecting bilinear pairings. Groth and Sahai showed that projecting bilinear pairings can be achieved in the prime-order group setting. They constructed both projecting asymmetric bilinear pairings and projecting symmetric bilinear pairings, where a bilinear pairing e is symmetric if it satisfies e(g,h)=e(h,g) for any group elements g and h; otherwise, it is asymmetric. In this paper, we provide impossibility results on projecting bilinear pairings in a prime-order group setting. More precisely, we specify the lower bounds of · the image size of a projecting asymmetric bilinear pairing · the image size of a projecting symmetric bilinear pairing · the computational cost for a projecting asymmetric bilinear pairing · the computational cost for a projecting symmetric bilinear pairing in a prime-order group setting naturally induced from the k-linear assumption, where the computational cost means the number of generic operations. Our lower bounds regarding a projecting asymmetric bilinear pairing are tight, i.e., it is impossible to construct a more efficient projecting asymmetric bilinear pairing than the constructions of Groth-Sahai and Freeman. However, our lower bounds regarding a projecting symmetric bilinear pairing differ from Groth and Sahai's results regarding a symmetric bilinear pairing results; We fill these gaps by constructing projecting symmetric bilinear pairings. In addition, on the basis of the proposed symmetric bilinear pairings, we construct more efficient instantiations of cryptosystems that essentially use the projecting symmetric bilinear pairings in a modular fashion. Example applications include new instantiations of the Boneh-Goh-Nissim cryptosystem, the Groth-Sahai non-interactive proof system, and Seo-Cheon round optimal blind signatures proven secure under the DLIN assumption. These new instantiations are more efficient than the previous ones, which are also provably secure under the DLIN assumption. These applications are of independent interest.