# Post-Quantum Digital Signature: Verkle-Based HORST
## 12 Conclusions  
Strong alternatives must be developed since quantum computing poses a serious threat to cryptography systems. The security of hash-based signature systems against quantum attacks makes them promising. In order to overcome performance constraints while preserving security, this study presents Verkle-based HORST, a novel improvement on conventional hash-based signatures. The method provides useful benefits for practical implementation by rethinking data structures. Verkle-based HORST offers significant efficiency gains, but it is challenging to put into practice. Compared to conventional hash-based systems, its constant-time verification (1.4 ms in preliminary testing) makes up for the computationally demanding polynomial operations required for key creation and signature. Blockchain applications can be developed by integration with emerging standards, such as Ethereum's Verkle trees, even though toolchain support is still evolving. For embedded or Internet of Things devices, the trade-offs are justified due to the scheme's compact proofs, which are 75% smaller than Merkle-based HORST, especially in bandwidth-constrained environments. Our main contribution is to replace traditional Merkle trees with Verkle trees, which achieve constant-sized proofs by using sophisticated polynomial commitment schemes. This architectural enhancement solves a number of persistent issues in hash-based encryption and provides numerous important advantages. Most significantly, this approach results in significantly lower signatures overall by reducing proof sizes from logarithmic to constant. This is particularly beneficial for bandwidth- or storage-constrained environments such as blockchain networks and IoT devices. Additionally, regardless of the system's size, the verification procedure becomes far more efficient, needing just constant-time operations. Verkle-based HORST is particularly well-suited for large-scale deployments and systems that need a lot of signatures because of these features. Future work will focus on adapting the fractal/hypertree approach to Verkle trees. Instead of splitting Merkle trees, we will explore how to split Verkle trees into smaller subtrees. This would preserve the system's rapid verification and help it to scale more easily. We will also consider techniques to maximize the cryptographic operations and possibly combine Verkle trees with other post-quantum schemes. In terms of security, our study demonstrates that Verkle-based HORST preserves the robust protective features of conventional hash-based schemes. The same cryptographic presumptions, particularly the binding property of the vector promises and the collision resistance of the underlying hash function, maintain the construction's security. The technique provides protection against both conventional and quantum adversaries by achieving existential unforgeability against selected message attacks (EUF-CMA), as shown by our formal security example. Our structure stands out as a strong contender for the post-quantum cryptography standardization initiatives now taking place globally due to this security assurance and the increased efficiency. Although the Verkle-based HORST has several benefits, polynomial commitments during key generation and signature processes result in computational complexity. Additional crypto analysis and performance benchmarking may be beneficial for Verkle trees, a novel cryptographic primitive. Conceptualization, M.I. ; methodology, M.I. and T.K. ; software, M.I. and T.K. ; validation, M.I., R.B. and T.K. ; formal analysis, M.I. and T.K. ; investigation, M.I. and T.K. ; resources, M.I., R.B. and T.K. ; data curation, T.K. ; writing--original draft preparation, T.K. ; writing--review and editing, M.I. and T.K. ; visualization, T.K. ; supervision, M.I., R.B. and T.K. ; project administration, M.I. ; funding acquisition, M.I. All authors have read and agreed to the published version of the manuscript.