Utilizing idle computing resources distributed worldwide to train large language models provides a novel paradigm for supplying computing power while helping to reduce training costs. A blockchain-based large model fine-tuning compute-power sharing platform, CompuDEX, was proposed to address the challenges of privacy risks, malicious attacks and lack of trust associated with this method. The trustless and anonymous nature of blockchain technology was leveraged to create a transaction platform that eliminated the need for trusted intermediaries while protecting user privacy. The smart contracts and cryptographic tools were employed to encourage fair competition among compute power providers, further reducing training costs. A security scheme combined with a “Red Balloon” incentive mechanism was designed based on zero-knowledge proofs to identify and penalize the malicious behaviors of compute power providers. The structure of the fine-tuning method LoRA was split to ensure data privacy during the training process without introducing additional computational overhead. Experimental results showed that during the forward propagation phase of fine-tuning, the computational cost was only 8% to 14% of that charged by major domestic cloud service providers. By increasing the number of parallel nodes, the execution time was significantly reduced from 175% of the local training time to 20% or even lower.