  With the rapid development of AI technology, we have witnessed numerous
innovations and conveniences. However, along with these advancements come
privacy threats and risks. Fully Homomorphic Encryption (FHE) emerges as a key
technology for privacy-preserving computation, enabling computations while
maintaining data privacy. Nevertheless, FHE has limitations in processing
continuous non-polynomial functions as it is restricted to discrete integers
and supports only addition and multiplication. Spiking Neural Networks (SNNs)
operate on discrete spike signals, naturally aligning with the properties of
FHE. In this paper, we present a framework called FHE-DiCSNN. This framework is
based on the efficient TFHE scheme and leverages the discrete properties of
SNNs to achieve high prediction performance on ciphertexts. Firstly, by
employing bootstrapping techniques, we successfully implement computations of
the Leaky Integrate-and-Fire neuron model on ciphertexts. Through
bootstrapping, we can facilitate computations for SNNs of arbitrary depth. This
framework can be extended to other spiking neuron models, providing a novel
framework for the homomorphic evaluation of SNNs. Secondly, inspired by CNNs,
we adopt convolutional methods to replace Poisson encoding. This not only
enhances accuracy but also mitigates the issue of prolonged simulation time
caused by random encoding. Furthermore, we employ engineering techniques to
parallelize the computation of bootstrapping, resulting in a significant
improvement in computational efficiency. Finally, we evaluate our model on the
MNIST dataset. Experimental results demonstrate that, with the optimal
parameter configuration, FHE-DiCSNN achieves an accuracy of 97.94% on
ciphertexts, with a loss of only 0.53% compared to the original network's
accuracy of 98.47%. Moreover, each prediction requires only 0.75 seconds of
computation time
