Vector and Functional Commitments from Lattices

Hoeteck Wee, David J. Wu

Hoeteck Wee, David J. Wu

Huang Lin

Maria Nuțu, Giorgi Akhalaia, Răzvan Bocu +1 more

Commitment schemes represent foundational cryptographic primitives enabling secure verification protocols across diverse applications, from blockchain systems to zero-knowledge proofs. This paper presents a systematic survey of vector, polynomial, and functional commitment schemes, analyzing their evolution from classical constructions to post-quantum secure alternatives. We examine the strengths and limitations of RSA-based, Diffie–Hellman, and lattice-based approaches, highlighting the critical shift toward quantum-resistant designs necessitated by emerging computational threats. The survey reveals that while lattice-based schemes (particularly those using the Short Integer Solution problem) offer promising security guarantees, they face practical challenges in proof size and verification efficiency. Functional commitments emerge as a powerful generalization, though their adoption is constrained by computational overhead and setup requirements. Key findings identify persistent gaps in adaptive security, composability, and real-world deployment, while proposed solutions emphasize optimization techniques and hybrid approaches. By synthesizing over 90 research works, this paper provides both a comprehensive reference for cryptographic researchers and a roadmap for future developments in commitment schemes, particularly in addressing the urgent demands of post-quantum cryptography and decentralized systems.

Karsten Balzer, M. Bönitz

Maksim Iavich, Nursulu A. Kapalova

Many public key cryptosystems in use today run the risk of being broken as quantum computing develops, affecting the security of popular commercial applications. Although there are possible defenses against quantum assaults, their complexity and inefficiency make them unsuitable for daily usage. This article discusses asymmetric hash-based digital signature algorithms, focusing on the symmetric and balanced structure achieved through the use of k-ary Verkle trees and lattice-based vector commitments. The study investigates the new concepts using vector commitments, a Verkle tree, and k-ary Verkle tree, which enhance efficiency and scalability while maintaining a symmetric structure in cryptographic proofs. Using cutting-edge Verkle tree technology, the authors of this paper provide a novel approach to creating a digital signature system. This is accomplished by using vector commitments, a k-ary Verkle tree, Verkle tree, and lattice-based vector commitments for post-quantum characteristics. The study also presents the ideas for designing post-quantum signatures using a k-ary Verkle tree, emphasizing the symmetry in tree structures and the balance between security and efficiency in asymmetric cryptographic systems.