Scientific collaborations benefit from collaborative learning of distributed sources, but remain difficult to achieve when data are sensitive. In recent years, privacy preserving techniques have been widely studied to analyze distributed data across different agencies while protecting sensitive information. Most existing privacy preserving techniques are designed to resist semi-honest adversaries and require intense computation to perform data analysis. Secure collaborative learning is significantly difficult with the presence of malicious adversaries who may deviates from the secure protocol. Another challenge is to maintain high computation efficiency with privacy protection. In this paper, matrix encryption is applied to encrypt data such that the secure schemes are against malicious adversaries, including chosen plaintext attack, known plaintext attack, and collusion attack. The encryption scheme also achieves local differential privacy. Moreover, cross validation is studied to prevent overfitting without additional communication cost. Empirical experiments on real-world datasets demonstrate that the proposed schemes are computationally efficient compared to existing techniques against malicious adversary and semi-honest model.