In recent years, more and more machine learning algorithms depend on the cloud computing. When a machine learning system is trained or classified in the cloud environment, the cloud server obtains data from the user side. Then, the privacy of the data depends on the service provider, it is easy to induce the malicious acquisition and utilization of data. On the other hand, the attackers can detect the statistical characteristics of machine learning data and infer the parameters of machine learning model through reverse attacks. Therefore, it is urgent to design an effective encryption scheme to protect the data’s privacy without breaking the performance of machine learning.

In this paper, we propose a novel homomorphic encryption framework over non-abelian rings, and define the homomorphism operations in ciphertexts space. The scheme can achieve one-way security based on the Conjugacy Search Problem. After that, a homomorphic encryption was proposed over a matrix-ring. It supports real numbers encryption based on the homomorphism of 2-order displacement matrix coding function and achieves fast ciphertexts homomorphic comparison without decrypting any ciphetexts operations’ intermediate result. Furthermore, we use the scheme to realize privacy preservation for machine learning training and classification in data ciphertexts environment. The analysis shows that our proposed schemes are efficient for encryption/decryption and homomorphic operations.

近年来，越来越多的机器学习算法依赖于云计算。在云环境中对机器学习系统进行培训或分类时，云服务器会从用户方获取数据。然后，数据的私密性取决于服务提供商，很容易诱发数据的恶意获取和利用。另一方面，攻击者可以检测机器学习数据的统计特征，并通过反向攻击来推断机器学习模型的参数。因此，迫切需要设计一种有效的加密方案来保护数据的私密性，同时又不影响机器学习的性能。

在本文中，我们提出了一种新的非阿贝尔环上的同态加密框架，并定义了密文空间中的同构操作。该方案可以基于共轭搜索问题实现单向安全性。此后，在矩阵环上提出了同态加密。它支持基于2阶位移矩阵编码功能的同态性的实数加密，并且无需解密任何密文运算的中间结果即可实现快速密文同态比较。此外，我们使用该方案在数据密文环境中实现机器学习训练和分类的隐私保护。分析表明，我们提出的方案对于加密/解密和同态运算是有效的。