NTRU Prime

Several ideal-lattice-based cryptosystems have been broken by recent attacks that exploit special structures of the rings used in those cryptosystems. The same structures are also used in the leading proposals for post-quantum lattice-based cryptography, including the classic NTRU cryptosystem and typical Ring-LWE-based cryptosystems. This paper proposes NTRU Prime, which tweaks NTRU to use rings without these structures; proposes Streamlined NTRU Prime, which optimizes NTRU Prime from an implementation perspective; finds highsecurity post-quantum parameters for Streamlined NTRU Prime; and optimizes a constant-time implementation of those parameters. The performance results are surprisingly competitive with the best previous speeds for lattice-based cryptography.