Fast Bootstrapping in Z_q

Abstract

In 2015, Ducas and Micciancio presented a novel technique to compute the NAND gate using the Learning With Errors cryptosystem (LWE), along with a novel bootstrapping technique that turns turns this cryptosystem into a fully-homomorphic encryption scheme that allows a very short and fast implementation. We present an extension of their bootstrapping technique that allows refreshing encryptions of elements in Z_p and the homomorphic computation of arbitrary gates, alongside with an implementation that exploits the power of parallel computation.