A blockchain as a trustworthy and secure decentralized and distributed network has been emerged for many applications such as in banking, finance, insurance, healthcare and business. Recently, many communities in blockchain networks want to deploy machine learning models to get meaningful knowledge from geographically distributed large-scale data owned by each participant. To run a learning model without data centralization, distributed machine learning (DML) for blockchain networks has been

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... died. While several works have been proposed, privacy and security have not been sufficiently addressed, and as we show later, there are vulnerabilities in the architecture and limitations in terms of efficiency. In this paper, we propose a privacy-preserving DML model for a permissioned blockchain to resolve the privacy, security, and performance issues in a systematic way. We develop a differentially private stochastic gradient descent method and an error-based aggregation rule as core primitives. Our model can treat any type of differentially private learning algorithm where non-deterministic functions should be defined. The proposed error-based aggregation rule is effective to prevent attacks by an adversarial node that tries to deteriorate the accuracy of DML models. Our experiment results show that our proposed model provides stronger resilience against adversarial attacks than other aggregation rules under a differentially private scenario. Finally, we show that our proposed model has high usability because it has low computational complexity and low transaction latency. INDEX TERMS Adversarial node, differential privacy, machine learning, permissioned blockchain.