Fractional Verkle Trees for Scalable Post-Quantum Signatures

Abstract

Quantum computers threaten to break widely used cryptosystems like RSA and ECC, forcing us to develop new quantum-resistant alternatives. While hash-based signatures like SPHINCS+ offer a proven solution, their reliance on Merkle trees result in large signature sizes and memory-intensive verification, which hinders scalability. We present a novel approach that replaces Merkle trees with Fractional Verkle Trees (FVTs), a hierarchical structure where a large Verkle tree is decomposed into smaller, more manageable pieces, which we call hypertrees. This approach provides fast verification and smaller signatures, while preserving the required level of security. Our FVT construction offers a useful basis for scalable verifiable data structures while lowering memory and verification costs without sacrificing security. Validation by way of a functional prototype shows that the derived Fractal Verkle-Based Digital Signature (FVDS) scheme achieves signature sizes of about 16.2 KB, which is 2.5× smaller than SPHINCS+, while maintaining localized updates and scalable verification. This makes it especially appropriate for bandwidth-constrained applications, such as IoT firmware updates and blockchain light clients.