Semi-homomorphic Encryption and Multiparty Computation

An additively-homomorphic encryption scheme enables us to compute linear functions of an encrypted input by manipulating only the ciphertexts. We define the relaxed notion of a semihomomorphic encryption scheme, where the plaintext can be recovered as long as the computed function does not increase the size of the input “too much”. We show that a number of existing cryptosystems are captured by our relaxed notion. In particular, we give examples of semi-homomorphic encryption schemes based on lattices, subset sum and factoring. We then demonstrate how semi-homomorphic encryption schemes allow us to construct an efficient multiparty computation protocol for arithmetic circuits, UC-secure against a dishonest majority. The protocol consists of a preprocessing phase and an online phase. Neither the inputs nor the function to be computed have to be known during preprocessing. Moreover, the online phase is extremely efficient as it requires no cryptographic operations: the parties only ...

• Type: Journal
• Year: 2011
• Where: EUROCRYPT
• Authors: Rikke Bendlin, Ivan Damgård, Claudio Orlandi, Sarah Zakarias
• Keywords: Arithmetic Circuits, Cryptology, EUROCRYPT 2011, Multiparty Computation, Subset Sum