Asynchronous verifiable information dispersal protocol of achieving optimal communication

The evolution of distributed systems necessitates robust protocols to facilitate secure and efficient data storage and retrieval amid challenges like asynchronous communication and adversarial threats. However, achieving the theoretical lower bounds of communication cost in Asynchronous Verifiable Information Dispersal (AVID) protocols remains an unresolved issue, prompting the need for innovation in this domain. In this paper, we propose a new AVID protocol designed to optimize communication cost. In contrast to previous approaches, we leverage vector commitment (VC) technology combined with erasure codes, replacing conventional hash tree structures or error correction codes. This approach results in significant O(logn) communication savings. Additionally, our research reveals that while ensuring simultaneous output from all honest nodes is desirable to satisfy Totality, it is not necessary for all nodes to receive corresponding shares or proofs during the Dispersal phase. This insight allows us to circumvent the common O(n(2)kappa) communication overhead. Our AVID protocol achieves an optimal dispersal cost of O(|M| + n(2)) compared to the prior best of O(|M| + kappa n(2)). Furthermore, each node in our protocol incurs a storage cost of O(|M|/n + kappa) bits, while the retrieval cost per client is O(|M| + n kappa).