Implementing Gentry's Fully-Homomorphic Encryption Scheme

We describe a working implementation of a variant of Gentry’s fully homomorphic encryption scheme (STOC 2009), similar to the variant used in an earlier implementation effort by Smart and Vercauteren (PKC 2010). Smart and Vercauteren implemented the underlying “somewhat homomorphic” scheme, but were not able to implement the bootstrapping functionality that is needed to get the complete scheme to work. We show a number of optimizations that allow us to implement all aspects of the scheme, including the bootstrapping functionality. Our main optimization is a key-generation method for the underlying somewhat homomorphic encryption, that does not require full polynomial inversion. This reduces the asymptotic complexity from ˜O(n2.5

• Type: Journal
• Year: 2011
• Where: EUROCRYPT
• Authors: Craig Gentry, Shai Halevi
• Keywords: Asymptotic Complexity, Cryptology, EUROCRYPT 2011, Generation Method, Key Generation