Abstract: The cross-domain recommendation (CDR) technique has been widely applied in recommendation systems and can effectively relieve the data sparsity and cold start problems. However, it brings up data privacy and authenticity challenges due to different data sources. Most existing solutions only consider data privacy, and are not robust against participant poisoning attacks that affect the quality of recommendations. How to leverage the privacy and authenticity of data remains a key challenge. To this end, we propose a blockchain-based anonymous model for CDR systems (BAM_CRS). Under this model, we use a three-chain structure to store users, products, and the relationships between the two parties to guarantee privacy. This structure enables transactions to be separated from users and items to guarantee privacy and to establish consensus without relying on a central authority. For data authenticity, we warrant data imtamability and traceability through on-chain data collection and design a contribution-based quantification and incentive mechanism to ensure system sustainability. Additionally, a signature-based verifiable mechanism is designed to motivate node participation and further guarantee data authenticity. Experiments on real-life datasets demonstrate that our model can protect privacy with an advantage of about 2% improvement over baselines in terms of precision and F1 metrics.