We propose an ensemble technique for converting any classifier into a computationally secure classifier. We define a simpler security problem for random binary classifiers and prove a reduction from this model to the security of the overall ensemble classifier. We provide experimental evidence of the security of our random binary classifiers, as well as empirical results of the adversarial accuracy of the overall ensemble to black-box attacks. Our construction crucially leverages hidden randomness in the multiclass-to-binary reduction.