NFLlib: NTT-Based Fast Lattice Library

Recent years have witnessed an increased interest in lattice cryptography. Besides its strong security guarantees, its simplicity and versatility make this powerful theoretical tool a promising competitive alternative to classical cryptographic schemes. In this paper, we introduce NFLlib, an efficient and open-source C++ library dedicated to ideal lattice cryptography in the widely-spread polynomial ring $$\mathbb Z_{p}[x]/x^n+1$$ for n a power of 2. The library combines algorithmic optimizations Chinese Remainder Theorem, optimized Number Theoretic Transform together with programming optimization techniques SSE and AVX2 specializations, C++ expression templates, etc., and will be fully available under an open source license. The library compares very favorably to other libraries used in ideal lattice cryptography implementations namely the generic number theory libraries NTL and flint implementing polynomial arithmetic, and the optimized library for lattice homomorphic encryption HElib: restricting the library to the aforementioned polynomial ring allows to gain several orders of magnitude in efficiency.