We present new speed records on the Arm-v8A architecture for the lattice-based schemes Dilithium, Kyber, and Saber. The core novelty in this paper is the combination of Montgomery multiplication and Barrett reduction resulting in “Barrett multiplication” which allows particularly efficient modular one-known-factor multiplication using the Arm-v8A Neon vector instructions. These novel techniques combined with fast two-unknown-factor Montgomery multiplication, Barrett reduction sequences, and interleaved multi-stage butterflies result in significantly faster code.
We also introduce “asymmetric multiplication” which is an improved technique for caching the results of the incomplete NTT, used e.g. for matrix-to-vector polynomial multiplication. Our implementations target the Arm Cortex-A72 CPU, on which our speed is 1.7× that of the state-of-the-art matrix-to-vector polynomial multiplication in Kyber [Nguyen-Gaj 2021]. For Saber, NTTs are far superior to Toom-Cook multiplication on the Arm-v8A architecture, outrunning the matrix-to-vector polynomial multiplication by 2.1×. On the Apple M1, our matrix-vector products run 2.1× and 1.9× faster for Kyber and Saber respectively.

By admin