i-Hop Homomorphic Encryption and Rerandomizable Yao Circuits

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 ...

• Type: Conference
• Year: 2010
• Where: CRYPTO
• Authors: Craig Gentry, Shai Halevi, Vinod Vaikuntanathan
• Keywords: CRYPTO 2010, Cryptology, Homomorphic Encryption, Homomorphic Encryption Scheme, Multi-hop Homomorphic Encryption