Flattening NTRU for Evaluation Key Free Homomorphic Encryption

Abstract

Abstract We propose a new FHE scheme F-NTRU that adopts the flattening technique proposed in GSW to derive an NTRU based scheme that (similar to GSW) does not require evaluation keys or key switching. Our scheme eliminates the decision small polynomial ratio assumption but relies only on the standard R-LWE assumption. It uses wide key distributions, and hence is immune to Subfield Lattice Attack. In practice, our scheme achieves competitive timings compared to the existing schemes. We are able to compute a homomorphic multiplication in 24.4 msec and 76.0 msec for 5 and 30 levels, respectively, without amortization. Furthermore, our scheme features small ciphertexts, e.g. 2376 KB for 30 levels. The assurance gained by using wide key distributions along with the message space flexibility of the scheme, i.e. bits, binary polynomials, and integers with a large message space, allows the use of the proposed scheme in a wide array of applications.