Speed up over the Rainbow

Nir Drucker, Shay Gueron

Abstract: Rainbow is a signature scheme that is based on multivariate polynomials. It is one of the Round-2 candidates of the NIST’s Post-Quantum Cryptography Standardization project. Its computations rely heavily on GF(2^8) arithmetic and the Rainbow submission optimizes the code by using AVX2 shuffle and permute instructions. In this paper, we show a new optimization that leverages: a) AVX512 architecture; b) the latest processor capabilities Galois Field New Instructions(GF-NI), available on Intel "Ice Lake" processor. We achieved a speedup of 2.43x/3.13x/0.64x for key generation/signing/verifying, respectively. We also propose a variation of Rainbow, with equivalent security, using a different representation of GF(2^8). With this variant, we achieve a speedup of 2.44x/4.7x/2.1x for key generation/signing/verifying, respectively.