Homomorphic Evaluation of Neural Networks Using Functional Bootstrapping with CKKS

In this work, the newly developed functional bootstrapping (FBT) for the Cheon–Kim–Kim–Song (CKKS) scheme is used for the first time to homomorphically evaluate an encrypted neural network. The advantage of FBT over previous approaches for the homomorphic evaluation of non-linear activation functions is that it combines bootstrapping and homomorphic function evaluation. For this purpose, FBT for CKKS is extended to be applied to real input values by evaluating the first order Hermite interpolation function not only on its interpolation points but on the entire domain [0,1]. For the sigmoid function, to respect the internal representation of negative values in CKKS and the convergence behaviour of trigonometric interpolation, a glueing of shifted and reflected sigmoid functions that is periodic and continuous is used as an input function for FBT. The experimental results yield an accuracy of 97.33% with a relative loss of 0% compared to the Hermite plaintext counterpart that were obtained with a fully connected neural network with 100 hidden neurons on the MNIST test set at a security level of 128 bits. The current implementation required approximately 1.66 s per image (amortised time) and about 201 GB RAM.