vCNN: Verifiable Convolutional Neural Network Based on zk-SNARKs

It is becoming important for the client to be able to check whether the AI inference services have been correctly calculated. Since the weight values in a CNN model are assets of service providers, the client should be able to check the correctness of the result without them. The Zero-knowledge Succinct Non-interactive Argument of Knowledge (zk-SNARK) allows verifying the result without input and weight values. However, the proving time in zk-SNARK is too slow to be applied to real AI applications. This article proposes a new efficient verifiable convolutional neural network (vCNN) framework that greatly accelerates the proving performance. We introduce a new efficient relation representation for convolution equations, reducing the proving complexity of convolution from O(ln) to O(l+n) compared to existing zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) approaches, where l and n denote the size of the kernel and the data in CNNs. Experimental results show that the proposed vCNN improves proving performance by 20-fold for a simple MNIST and 18,000-fold for VGG16. The security of the proposed scheme is formally proven.