Privacy-preserving computation (PPC) methods, such as secure multiparty computation (MPC) and homomorphic encryption (HE), are deployed increasingly often to guarantee data confidentiality in computations over private, distributed data. Similarly, we observe a steep increase in the adoption of zero-knowledge proofs (ZKPs) to guarantee (public) verifiability of locally executed computations. We project that applications that are data intensive and require strong privacy guarantees, are also likely to require correctness guarantees, especially when outsourced. While the combination of methods for verifiability and privacy protection has clear benefits, certain challenges stand before their widespread practical adoption. In this work, we analyze existing solutions that combine verifiability with privacy-preserving computations over distributed data, in order to preserve confidentiality and guarantee correctness at the same time.We classify and compare 32 different schemes, regarding solution approach, security, efficiency, and practicality. Lastly, we discuss some of the most promising solutions in this regard, and present various open challenges and directions for future research.

翻译：隐私保护计算（PPC）方法，如安全多方计算（MPC）和同态加密（HE），正日益广泛地部署于私有分布式数据的计算场景中，以保障数据机密性。与此同时，我们观察到零知识证明（ZKPs）的采用率急剧上升，用于保证本地执行计算的（公开）可验证性。我们预计，那些数据密集且需要强隐私保证的应用程序，同样可能要求正确性保证，尤其是在外包场景下。尽管将可验证性与隐私保护方法相结合具有明显优势，但其广泛实际应用仍面临若干挑战。本文分析了现有将可验证性与分布式数据隐私保护计算相结合的方案，旨在同时保障机密性与正确性。我们对32种不同方案进行了分类与比较，涵盖解决思路、安全性、效率及实用性等方面。最后，我们讨论了该领域最具前景的若干方案，并指出了当前存在的多种开放性挑战及未来研究方向。