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Modern implementations of homomorphic encryption (HE) rely heavily onpolynomial arithmetic over a finite field. This is particularly true of theCKKS, BFV, and BGV HE schemes. Two of the biggest performance bottlenecks in HEprimitives and applications are polynomial modular multiplication and theforward and inverse number-theoretic transform (NTT). Here, we introduce IntelHomomorphic Encryption Acceleration Library (Intel HEXL), a C++ library whichprovides optimized implementations of polynomial arithmetic for Intelprocessors. Intel HEXL takes advantage of the recent Intel Advanced VectorExtensions 512 (Intel AVX512) instruction set to provide state-of-the-artimplementations of the NTT and modular multiplication. On the forward andinverse NTT, Intel HEXL provides up to 7.2x and 6.7x speedup, respectively,over a native C++ implementation. Intel HEXL also provides up to 6.0x speedupon the element-wise vector-vector modular multiplication, and 1.7x speedup onthe element-wise vector-scalar modular multiplication. Intel HEXL is availableopen-source at https://github.com/intel/hexl under the Apache 2.0 license andhas been adopted by the Microsoft SEAL and PALISADE homomorphic encryptionlibraries.

Intel HEXL: Accelerating Homomorphic Encryption with Intel AVX512-IFMA52