Privacy Preservation for Machine Learning Training and Classification Based on Homomorphic Encryption Schemes

•This work presented a novel homomorphic encryption framework over non-abelian rings (matrix-ring). It is one-way secure based on the Conjugacy Search Problem.•The scheme supports real numbers encryption and achieves fast ciphertexts homomorphic comparison without decrypting any ciphetexts operations’s intermediate result.•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.