  This paper introduces stochastic sparse adversarial attacks (SSAA), standing
as simple, fast and purely noise-based targeted and untargeted attacks of
neural network classifiers (NNC). SSAA offer new examples of sparse (or $L_0$)
attacks for which only few methods have been proposed previously. These attacks
are devised by exploiting a small-time expansion idea widely used for Markov
processes. Experiments on small and large datasets (CIFAR-10 and ImageNet)
illustrate several advantages of SSAA in comparison with the-state-of-the-art
methods. For instance, in the untargeted case, our method called Voting Folded
Gaussian Attack (VFGA) scales efficiently to ImageNet and achieves a
significantly lower $L_0$ score than SparseFool (up to $\frac{2}{5}$) while
being faster. Moreover, VFGA achieves better $L_0$ scores on ImageNet than
Sparse-RS when both attacks are fully successful on a large number of samples.
