Privacy-preserving Principal Component Analysis Based on Homomorphic Encryption
In real life,data is not interconnected between different industries,or even between different departments within the same industry.With the improvement of computer computing power,it is not computing power but data volume that restricts the effectiveness of model training.Therefore,in order to obtain a better algorithm model,relying solely on one party's data is not enough.It needs the participation of two or more parties,which requires privacy protection for all parties.In addition,as data col-lection becomes more detailed,the data dimension also increases.For high dimension data,dimension reduction is an indispensable step.And in terms of dimension reduction,principal component analysis(PCA)is a commonly used method.Homomorphic en-cryption is a solution when two parties want to collaborate on privacy protection data dimension reduction.Homomorphic encryp-tion can compute encrypted data while protecting data privacy,and can be used to compute the PC A on encrypted data.In this pa-per,a two party encrypted data PCA scheme is designed using the CKKS homomorphic encryption scheme and the power method for dominant eigenvectors,achieving the goal of dimension reduction while protecting the privacy of both parties'data.By impro-ving the traditional power method iteration steps,the expensive homomorphic ciphertext division is avoided,allowing for more iterations with small encryption parameters,thereby reducing the computing time and improving the accuracy of the computed re-sults.Through testing on public datasets and comparing it with some existing schemes,the scheme reduces the computational time by about 80％,and reduces the mean squared error to within 1％compared to the plaintext computation results.
Homomorphic encryptionPrivacy preservingPrincipal component analysisSingular value decompositionPower method
万方数据
维普
