Hercules: Boosting the Performance of Privacy-Preserving Federated Learning

In this paper, we address the problem of privacy-preserving federated neural network training with
$N$
users. We present
Hercules
, an efficient and high-precision training framework that can tolerate collusion of up to
$N-1$
users.
Hercules
follows the POSEIDON framework proposed by Sav et al. (NDSS’21), but makes a qualitative leap in performance with the following contributions: (i) we design a novel parallel homomorphic computation method for matrix operations, which enables fast Single Instruction and Multiple Data (SIMD) operations over ciphertexts. For the multiplication of two
$h\times h$
dimensional matrices, our method reduces the computation complexity from
$O(h^{3})$
to
$O(h)$
. This greatly improves the training efficiency of the neural network since the ciphertext computation is dominated by the convolution operations; (ii) we present an efficient approximation on the sign function based on the composite polynomial approximation. It is used to approximate non-polynomial functions (i.e.,
ReLU
and
max
), with the optimal asymptotic complexity. Extensive experiments on various benchmark datasets (BCW, ESR, CREDIT, MNIST, SVHN, CIFAR-10 and CIFAR-100) show that compared with POSEIDON,
Hercules
obtains up to 4% increase in model accuracy, and up to
$60\times$
reduction in the computation and communication cost.