A new public key cryptosystem based on higher residues
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Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
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PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Verifiable secret-ballot elections
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The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
A Public Key Cryptosystem Based On A Subgroup Membership Problem
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Fully homomorphic encryption using ideal lattices
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Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Predicate encryption supporting disjunctions, polynomial equations, and inner products
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
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IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
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TCC'11 Proceedings of the 8th conference on Theory of cryptography
Efficient Fully Homomorphic Encryption from (Standard) LWE
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
(Leveled) fully homomorphic encryption without bootstrapping
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Symmetric subgroup membership problems
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
An oblivious transfer protocol with log-squared communication
ISC'05 Proceedings of the 8th international conference on Information Security
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
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
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
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We propose a generic approach to design homomorphic encryption schemes, which extends Gjøsteen's framework. From this generic method, we deduce a new homomorphic encryption scheme in a composite-order subgroup of points of an elliptic curve which admits a pairing e: G×G→Gt. This scheme has some interesting theoretical and practical properties: it allows an arbitrary number of multiplications in the groups GandGt, as well as a pairing evaluation on the underlying plaintexts. We prove the semantic security under chosen plaintext attack of our scheme under a generalized subgroup membership assumption, and we also prove that it cannot achieve ind-cca1 security. We eventually propose an original application to shared decryption. On the theoretical side, this scheme is an example of cryptosystem which can be naturally implemented with groups of prime order, as the homomorphic properties require only a projecting pairing using Freeman's terminology. However the application to shared decryption also relies on the fact that the pairing is cancelling and therefore does not survive this conversion.