  Machine learning models are vulnerable to simple model stealing attacks if
the adversary can obtain output labels for chosen inputs. To protect against
these attacks, it has been proposed to limit the information provided to the
adversary by omitting probability scores, significantly impacting the utility
of the provided service. In this work, we illustrate how a service provider can
still provide useful, albeit misleading, class probability information, while
significantly limiting the success of the attack. Our defense forces the
adversary to discard the class probabilities, requiring significantly more
queries before they can train a model with comparable performance. We evaluate
several attack strategies, model architectures, and hyperparameters under
varying adversarial models, and evaluate the efficacy of our defense against
the strongest adversary. Finally, we quantify the amount of noise injected into
the class probabilities to mesure the loss in utility, e.g., adding 1.26 nats
per query on CIFAR-10 and 3.27 on MNIST. Our evaluation shows our defense can
degrade the accuracy of the stolen model at least 20%, or require up to 64
times more queries while keeping the accuracy of the protected model almost
intact.
