Spiking Neural Networks are a class of artificial neural networks that process information as discrete spikes. The time and energy consumed in SNN implementations is strongly dependent on the number of spikes processed. We explore this sensitivity from an adversarial perspective and propose SpikeAttack, a completely new class of attacks on SNNs. SpikeAttack impacts the efficiency of SNNs via imperceptible perturbations that increase the overall spiking activity of the network, leading to increased time and energy consumption. Across four SNN benchmarks, SpikeAttackresults in 1.7x-2.5X increase in spike activity, leading to increases of 1.6x-2.3x and 1.4x-2.2x in latency and energy consumption, respectively.