CRT-Based Parallel Residue Transmission for Distributed Edge Blockchain Computing: A Scalable IoT Cluster Architecture for Arid Agriculture

This paper presents a distributed edge computing framework for resource-constrained IoT clusters that employs Chinese Remainder Theorem (CRT) basedparallel residue transmission to reduce communication latency and energy overhead. The architecture comprises 50 ESP32 nodes and a 4-node Raspberry Pi4B cluster running Hyperledger Fabric with Raft consensus. CRT decomposition reduces effective latency from 372ms sequential to 124ms parallel (66.7%reduction) with O(k) complexity and lower memory footprint than compression baselines. The blockchain layer sustains 63TPS with 1.7s latency and 99.4% integrity on ARM64 hardware. Scalability analysis shows a theoretical nodecapacity of 484 full readings under LoRa parameters (and packet capacity of1,451 CRT residue packets), with latency constant below saturation and degrad-ing predictably under an M/D/1 queuing model. The framework was validated ina 61 day agricultural deployment, confirming its suitability for largescale heterogeneous IoT environments requiring lowpower sensing, distributed verification,and resilient edge actuation.