Abstract
This paper proposes a novel approach to designing modern digital signature schemes using Verkle trees and vector commitments based on the Chinese Remainder Theorem. Verkle trees enable efficient data structuring and optimization of verification processes, while vector commitments are aimed at securely binding information. The Chinese Remainder Theorem (CRT) is used to solve systems of congruences and allows for finding unique integer solutions given a set of remainders. In cryptographic schemes, CRT can be employed to accelerate computations and enhance performance. In the context of digital signatures, the Chinese Remainder Theorem contributes to improving algorithmic efficiency as well as ensuring security and resistance to various types of attacks. Additionally, the paper examines methods for enhancing system security through the use of hash functions. The proposed techniques enable the development of compact, efficient, and post-quantum-resistant cryptographic solutions.