A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Replication is not needed: single database, computationally-private information retrieval
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Computational complexity: a conceptual perspective
ACM SIGACT News
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Single database private information retrieval implies oblivious transfer
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
i-hop homomorphic encryption and rerandomizable Yao circuits
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Fully homomorphic encryption over the integers
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Bounded-Collusion IBE from key homomorphism
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Polly cracker, revisited, revisited
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Protecting data confidentiality in cloud systems
Proceedings of the Fourth Asia-Pacific Symposium on Internetware
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We show how to transform any additively homomorphic private-key encryption scheme that is compact, into a public-key encryption scheme. By compact we mean that the length of a homomorphically generated encryption is independent of the number of ciphertexts from which it was created. We do not require anything else on the distribution of homomorphically generated encryptions (in particular, we do not require them to be distributed like real ciphertexts). Our resulting public-key scheme is homomorphic in the following sense. If the private-key scheme is i+1-hop homomorphic with respect to some set of operations then the public-key scheme we construct is i-hop homomorphic with respect to the same set of operations.