HBSS: (simple) Hash-Based Stateless Signatures – Hash All the Way to the Rescue!

Recent advancements in post-Quantum secure signing have revitalized interest in one-time signatures, such as Lamport's, and their many signature extensions. Predominantly based on standard hash functions, these signatures avoid reliance on number theoretic assumptions. Existing methods utilize a commitment array, with de-commitment contingent on the hashed message's representation bits. State-of-the-art variants incorporate pseudorandom functions. This study introduces a novel method utilizing a probabilistic ''set membership data structure" derived from hash functions. It involves accessing a long array with $k$ independent hash functions for each message, analogous to Bloom filters. This stateless signature scheme is adjustable to accommodate any pre-set maximum number of signatures by modulating the array's length. The key concept is the partial loading of the de-committed array, ensuring validation of signed messages, non-validation of unsigned messages, and signature unforgeability (forgery equates to decommitment without the private key). This approach extends to improving one-time or bounded-message Constructions, like the Naor-Yung extension, for regular signature applications in the new Hash-Based Stateless Signature (HBSS) scheme.