Abstract
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.