Parallel Implementation of SPHINCS+ With GPUs

SPHINCS+ was selected as one of NIST Post-Quantum Cryptography Digital Signature Algorithms (PQC-DSA). However, SPHINCS+ processes are slower compared to other PQC-DSA. When integrating it into protocols (
$e.g.$
, TLS and IPSec), optimization research from the server perspective becomes crucial. Therefore, we present highly parallel and optimized implementations of SPHINCS+ on various NVIDIA GPU architectures (Pascal, Turing, and Ampere). We discovered parts within the internal processes of SPHINCS+ that could be parallelized and optimized them (
$e.g.$
, leaf node generation and node merging process in MSS, subtree constructions in FORS, signature generation in WOTS+ and hypertree layer construction), leveraging the characteristics of GPU architecture (
$e.g.$
, warp-based execution and efficient memory access). As far as we know, this is the first SPHINCS+ implementations on GPUs. Our implementations achieve 44,391(resp. 24,997 and 11,401) signature generations, 725,118(resp. 354,309 and 100,168) key generations, and 285,680(resp. 155,800 and 106,280) verifications per second at security level 1(resp. 3 and 5) on RTX3090. Furthermore, on GTX1070, our SPHINCS+ shows an enhanced throughput of
$\times 2.10$
for signature generation,
$\times 1.03$
for key generation, and
$\times 9.86$
for verification at security level 1, surpassing the study conducted by Sun
$et ~al.$
(IEEE TPDS 2020) on the GTX1080 having 640 more cores than GTX1070.