I'm solving a kernel ridge regression through a federated learning way. Equation to solve the kernel ridge regerssion is dot((K+lambdaI)^-1,y). So the aggregator of the problem knows the matrix A=(K+lambdaI)^-1.
But it cannot know the value of the labels y. So my idea was to encrypt the vector of labels y and apply inner product encrypton between the rows of the matrix and the encrypted vector. https://eprint.iacr.org/2015/017.pdf
Could I do the Setup,an Encryption of vector y just once, and then apply the KeyDer(msk,row of matrix) and Decryption for each row of the matrix? Or should I update the setup and encryption part each time?
If the dimension of the matrix is like 10k, or even 50k sometimes, do you think it could work? Otherwise, do you know other encryption technique to solve this problem?