CUSPX: Efficient GPU Implementations of Post-Quantum Signature SPHINCS+

Quantum computers pose a serious threat to existing cryptographic systems. While Post-Quantum Cryptography (PQC) offers resilience against quantum attacks, its performance limitations often hinder widespread adoption. Among the three National Institute of Standards and Technology (NIST)-selected general-purpose PQC schemes, SPHINCS${}^{+}$ is particularly susceptible to these limitations. We introduce CUSPX (CUDA SPHINCS ${}^{+}$), the first large-scale parallel implementation of SPHINCS${}^{+}$ capable of running across 10,000 cores. CUSPX leverages a novel three-level parallelism framework, applying it to algorithmic parallelism, data parallelism, and hybrid parallelism. Notably, CUSPX introduces parallel Merkle tree construction algorithms for arbitrary parallel scales and several load-balancing solutions, further enhancing performance. By treating tasks parallelism as the top level of parallelism, CUSPX provides a four-level parallel scheme that can run with any number of tasks. Evaluated on a single GeForce RTX 3090 using the SPHINCS${}^{+}$-SHA-256-128s-simple parameter set, CUSPX achieves a single task's signature generation latency of 0.67 ms, demonstrating a 5,105$\times$ speedup over a single-thread version and an 18.50$\times$ speedup over the previous fastest implementation.