In this paper, we present an approach which relies on the use of random noises to generate adversarial examples of deep neural network classifiers. We argue that existing deterministic attacks, which perform by sequentially applying maximal perturbations on selected components of the input, fail at reaching accurate adversarial examples on real-world large scale datasets. By exploiting a simple Taylor expansion of the expected output probability under the noise perturbation, we introduce noise-based sparse (or L0) targeted and untargeted attacks. Our proposed method, called Voting Folded Gaussian Attack (VFGA), achieves significantly better L0 scores than state-of-the-art L0 attacks (such as SparseFool and Sparse-RS) while being faster on both CIFAR-10 and ImageNet. Moreover, we show that VFGA is also applicable as an L∞ attack and outperforms the state-of-the-art projected gradient attack (PGD) method.