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 ( CU DA SP HIN CS ${}^{+}$ ), 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.