Better Bootstrapping in Fully Homomorphic Encryption
Gentry's bootstrapping technique is currently the only known method of obtaining a "Pure" Fully Homomorphic Encryption (FHE) schemes, and it may offers performance advantages even in cases that do not require pure FHE. The main bottleneck in bootstrapping is the need to evaluate homomorphically the reduction of one integer modulo another. This is typically done by emulating a binary modular reduction circuit, using bit operations on binary representation of integers. The authors present a simpler approach that bypasses the homomorphic modular-reduction bottleneck to some extent, by working with a modulus very close to a power of two.