Abstract
This paper addresses the problem of constructing post-quantum authenticated data structures for secure distributed information systems operating under potential quantum and cyber threats. The primary focus is on the development of a Verkle tree based on lattice vector commitments, providing compact proof structures, support for local updates, and resistance to quantum attacks. Particular attention is given to the local update propagation mechanism, which enables modification of commitments and proofs without full recomputation of the tree. The proposed approach reduces computational overhead during data updates and improves the efficiency of distributed storage systems operating under limited computational resources and unstable communication channels. The proposed scheme can be applied in secure distributed storage systems, cyber defense infrastructures, and protected communication environments requiring post-quantum security guarantees.