We show how a malicious learner can plant an undetectable backdoor into a classifier. On the surface, such a backdoored classifier behaves normally, but in reality, the learner maintains a mechanism for changing the classification of any input, with only a slight perturbation. Importantly, without the appropriate “backdoor key,” the mechanism is hidden and cannot be detected by any computationally-bounded observer. We demonstrate two frameworks for planting undetectable backdoors, with incomparable guarantees.•First, we show how to plant a backdoor in any model, using digital signature schemes. The construction guarantees that given query access to the original model and the backdoored version, it is computationally infeasible to find even a single input where they differ. This property implies that the backdoored model has generalization error comparable with the original model. Moreover, even if the distinguisher can request backdoored inputs of its choice, they cannot backdoor a new input—a property we call non-replicability.•Second, we demonstrate how to insert undetectable backdoors in models trained using the Random Fourier Features (RFF) learning paradigm (Rahimi, Recht; NeurIPS 2007). In this construction, undetectability holds against powerful white-box distinguishers: given a complete description of the network and the training data, no efficient distinguisher can guess whether the model is “clean” or contains a backdoor.
Our construction of undetectable backdoors also sheds light on the related issue of robustness to adversarial examples. In particular, by constructing undetectable backdoor for an “adversarially-robust” learning algorithm, we can produce a classifier that is indistinguishable from a robust classifier, but where every input has an adversarial example! In this way, the existence of undetectable backdoors represent a significant theoretical roadblock to certifying adversarial robustness.