Shorter Hash-Based Signatures Using Forced Pruning

The stateless hash-based digital signature algorithm (SLH-DSA) is a post-quantum signature scheme based on the SPHINCS$^+$ framework that was recently standardized by NIST. Although it offers many benefits, a drawback of SLH-DSA is that it has relatively large signatures. Several techniques have been proposed to reduce the signature size of SPHINCS-like schemes, and NIST is actively evaluating variants with shorter signatures for possible future standardization.

We explore using forced pruning in the few-time signature scheme used by SPHINCS$^+$ to reduce the overall signature size. Prior work suggested similar ideas, but claimed that the improvement from forced pruning was small. We re-visit this conclusion by performing a detailed theoretical analysis of forced pruning along with a more thorough exploration of its benefits. We show that forced pruning can improve upon SPHINCS+C (Oakland 2023) in all respects, and can reduce the overall signature size for the "smaller SPHINCS$^+$" variants proposed by Fluhrer and Dang by up to 20% with minimal effect on signing time. Our results thus show that forced pruning can be a beneficial optimization for hash-based signatures.