  Deep Neural Networks (DNNs) and Spiking Neural Networks (SNNs) are both known
for their susceptibility to adversarial attacks. Therefore, researchers in the
recent past have extensively studied the robustness and defense of DNNs and
SNNs under adversarial attacks. Compared to accurate SNNs (AccSNN), approximate
SNNs (AxSNNs) are known to be up to 4X more energy-efficient for ultra-low
power applications. Unfortunately, the robustness of AxSNNs under adversarial
attacks is yet unexplored. In this paper, we first extensively analyze the
robustness of AxSNNs with different structural parameters and approximation
levels under two gradient-based and two neuromorphic attacks. Then, we propose
two novel defense methods, i.e., precision scaling and approximate
quantization-aware filtering (AQF), for securing AxSNNs. We evaluated the
effectiveness of these two defense methods using both static and neuromorphic
datasets. Our results demonstrate that AxSNNs are more prone to adversarial
attacks than AccSNNs, but precision scaling and AQF significantly improve the
robustness of AxSNNs. For instance, a PGD attack on AxSNN results in a 72\%
accuracy loss compared to AccSNN without any attack, whereas the same attack on
the precision-scaled AxSNN leads to only a 17\% accuracy loss in the static
MNIST dataset (4X robustness improvement). Similarly, a Sparse Attack on AxSNN
leads to a 77\% accuracy loss when compared to AccSNN without any attack,
whereas the same attack on an AxSNN with AQF leads to only a 2\% accuracy loss
in the neuromorphic DVS128 Gesture dataset (38X robustness improvement).
