Efficient oblivious transfer protocols
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
One-Round Secure Computation and Secure Autonomous Mobile Agents
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Priced Oblivious Transfer: How to Sell Digital Goods
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Replication is not needed: single database, computationally-private information retrieval
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Non-Interactive CryptoComputing For NC1
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Circular-Secure Encryption from Decision Diffie-Hellman
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
A Proof of Security of Yao’s Protocol for Two-Party Computation
Journal of Cryptology
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Public-Key Cryptosystems Resilient to Key Leakage
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Evaluating branching programs on encrypted data
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Additively homomorphic encryption with d-operand multiplications
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Fully homomorphic encryption over the integers
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Bounded key-dependent message security
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Homomorphic encryption: from private-key to public-key
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Efficient non-interactive secure computation
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Can code polymorphism limit information leakage?
WISTP'11 Proceedings of the 5th IFIP WG 11.2 international conference on Information security theory and practice: security and privacy of mobile devices in wireless communication
Benaloh's dense probabilistic encryption revisited
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Secure computation on the web: computing without simultaneous interaction
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Generalized learning problems and applications to non-commutative cryptography
ProvSec'11 Proceedings of the 5th international conference on Provable security
Targeted malleability: homomorphic encryption for restricted computations
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
On constructing homomorphic encryption schemes from coding theory
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Multiparty computation with low communication, computation and interaction via threshold FHE
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Reaction attack on outsourced computing with fully homomorphic encryption schemes
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
Protecting data confidentiality in cloud systems
Proceedings of the Fourth Asia-Pacific Symposium on Internetware
Canon-MPC, a system for casual non-interactive secure multi-party computation using native client
Proceedings of the 12th ACM workshop on Workshop on privacy in the electronic society
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Homomorphic encryption (HE) schemes enable computing functions on encrypted data, by means of a public Eval procedure that can be applied to ciphertexts. But the evaluated ciphertexts so generated may differ from freshly encrypted ones. This brings up the question of whether one can keep computing on evaluated ciphertexts. An i-hop homomorphic encryption scheme is one where Eval can be called on its own output up to i times, while still being able to decrypt the result. A multi-hop homomorphic encryption is a scheme which is i-hop for all i. In this work we study i-hop and multi-hop schemes in conjunction with the properties of function-privacy (i.e., Eval's output hides the function) and compactness (i.e., the output of Eval is short). We provide formal definitions and describe several constructions. First, we observe that "bootstrapping" techniques can be used to convert any (1-hop) homomorphic encryption scheme into an i-hop scheme for any i, and the result inherits the function-privacy and/or compactness of the underlying scheme. However, if the underlying scheme is not compact (such as schemes derived from Yao circuits) then the complexity of the resulting i-hop scheme can be as high as nO(i). We then describe a specific DDH-based multi-hop homomorphic encryption scheme that does not suffer from this exponential blowup. Although not compact, this scheme has complexity linear in the size of the composed function, independently of the number of hops. The main technical ingredient in this solution is a re-randomizable variant of the Yao circuits. Namely, given a garbled circuit, anyone can re-garble it in such a way that even the party that generated the original garbled circuit cannot recognize it. This construction may be of independent interest.