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.

Among the zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARK), the simulation-extractable zk-SNARK (SE-SNARK) introduces a security notion of non-malleability. The existing pairing-based zk-SNARKs designed from linear encoding are known to be vulnerable to algebraic manipulation of the proof. The latest SE-SNARKs check the proof consistency by increasing the proof size and the verification cost. In particular, the number of pairings increases almost doubles due to further verification. In this paper, we propose two novel SE-SNARK constructions with a single verification. The consistency check is subsumed in a single verification through employing a hash function. The proof size and verification time of the proposed SE-SNARK schemes are minimal in that it is the same as the state-of-the-art zk-SNARK without non-malleability. The proof in our SE-SNARK constructions comprises only three group elements (type III) in the QAP-based scheme and two group elements (type I) in the SAP-based scheme. The verification time in both requires only 3 pairings. The soundness of the proposed schemes is proven under the hash-algebraic knowledge (HAK) assumption and the (linear) collision-resistant hash assumption.

With the rapid growth of the blockchain market, privacy and security issues for digital assets are becoming more important. In the most widely used public blockchains, such as Bitcoin and Ethereum, all activities on user accounts are publicly disclosed, which violates privacy regulations such as EU GDPR. Encryption of accounts and transactions may protect privacy, but it also raises issues of validity and transparency. While encrypted information can protect privacy, it cannot alone verify the validity of a transaction. Additionally, encryption makes it difficult to meet anti-money laundering regulations, such as auditability. In this paper, we propose Azeroth, an auditable zero-knowledge transfer framework. Azeroth connects a zero-knowledge proof to an encrypted transaction, enabling it to check its validation while protecting its privacy. Azeroth also allows authorized auditors to audit transactions. Azeroth is designed as a smart contract for flexible deployment on existing blockchains.We implement the Azeroth smart contract, execute it on various platforms including an Ethereum testnet blockchain, and measure the time to show the practicality of our proposal. The end-to-end latency of a privacy-preserving transfer takes about 4.4s. In particular, the client’s transaction generation time with a proof only takes about 0.9s. The security of Azeroth is proven under the cryptographic assumptions.