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Abstract We propose a generic compiler that can convert any zero-knowledge (ZK) proof for SIMD circuits to general circuits efficiently, and an extension that can preserve the space complexity of the proof systems. Our compiler can immediately produce new results improving upon state of the art.By plugging in our compiler to Antman, an interactive sublinear-communication protocol, we improve the overall communication complexity for general circuits from$$\mathcal {O}(C^{3/4})$$ $O\left(C^{3/4}\right)$to$$\mathcal {O}(C^{1/2})$$ $O\left(C^{1/2}\right)$. Our implementation shows that for a circuit of size$$2^{27}$$ $2^{27}$, it achieves up to$$83.6\times $$ $83.6\times$improvement on communication compared to the state-of-the-art implementation. Its end-to-end running time is at least$$70\%$$ $70\%$faster in a 10Mbps network.Using the recent results on compressed$$\varSigma $$ $\Sigma$-protocol theory, we obtain a discrete-log-based constant-round zero-knowledge argument with$$\mathcal {O}(C^{1/2})$$ $O\left(C^{1/2}\right)$communication and common random string length, improving over the state of the art that has linear-size common random string and requires heavier computation.We improve the communication of a designatedn-verifier zero-knowledge proof from$$\mathcal {O}(nC/B+n^2B^2)$$ $O(nC/B+n^2{B}^2)$to$$\mathcal {O}(nC/B+n^2)$$ $O(nC/B+n^2)$.To demonstrate the scalability of our compilers, we were able to extract a commit-and-prove SIMD ZK from Ligero and cast it in our framework. We also give one instantiation derived from LegoSNARK, demonstrating that the idea of CP-SNARK also fits in our methodology. 

Reconstructing 3D faces with facial geometry from single images has allowed for major advances in animation, generative models, and virtual reality. However, this ability to represent faces with their 3D features is not as fully explored by the facial expression inference (FEI) community. This study therefore aims to investigate the impacts of integrating such 3D representations into the FEI task, specifically for facial expression classification and face-based valence-arousal (VA) estimation. To accomplish this, we first assess the performance of two 3D face representations (both based on the 3D morphable model, FLAME) for the FEI tasks. We further explore two fusion architectures, intermediate fusion and late fusion, for integrating the 3D face representations with existing 2D inference frameworks. To evaluate our proposed architecture, we extract the corresponding 3D representations and perform extensive tests on the AffectNet and RAF-DB datasets. Our experimental results demonstrate that our proposed method outperforms the state-of-the-art AffectNet VA estimation and RAF-DB classification tasks. Moreover, our method can act as a complement to other existing methods to boost performance in many emotion inference tasks.