We propose a new defense mechanism against adversarial at-tacks inspired by an optical co-processor, providing robustness without compromising natural accuracy in both white-box and black-box settings. This hardware co-processor performs a nonlinear fixed random transformation, where the parameters are unknown and impossible to retrieve with sufficient precision for large enough dimensions. In the white-box setting, our defense works by obfuscating the parameters of the random projection. Unlike other defenses relying on obfuscated gradients, we find we are unable to build a re-liable backward differentiable approximation for obfuscated parameters. Moreover, while our model reaches a good natural accuracy with a hybrid backpropagation - synthetic gradient method, the same approach is suboptimal if employed to generate adversarial examples. Finally, our hybrid training method builds robust features against black-box and transfer attacks. We demonstrate our approach on a VGG-like architecture, placing the defense on top of the convolutional features, on CIFAR-10 and CIFAR-100.