Privacy-enhancing technologies (PETs), such as secure multi-party 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. While the combination of methods for (public) verifiability and privacy protection has clear significance, many attempts are far from practical adoption. In this work, we analyze existing solutions that add (public) verifiability to privacy-preserving computations over distributed data, in order to preserve confidentiality and guarantee correctness. To determine the required security and usability properties and whether these are satisfied, we look at various application areas including verifiable outsourcing, distributed ledger technology (DLT), and genomics. We then classify the solutions and describe frequently used approaches as well as efficiency metrics. Last but not least, we identify open challenges and discuss directions for future research that make verifiable, privacy-preserving computations more secure, efficient, and applicable in the real world.

翻译：隐私增强技术（如安全多方计算和同态加密）正日益广泛地部署于私有分布式数据的计算中，用以保障数据机密性。与此同时，我们观察到零知识证明的应用急剧增长，以确保本地执行计算的可（公开）验证性。我们预测，数据密集型且要求强隐私保护的应用，同样很可能需要正确性保证。尽管（公开）可验证性与隐私保护方法的结合具有明确意义，但许多尝试远未达到实际应用水平。本文分析了为分布式数据上的隐私保护计算增加（公开）可验证性的现有解决方案，以在保护机密性的同时确保正确性。为确定所需的安全性和可用性属性及其满足情况，我们考察了包括可验证外包、分布式账本技术和基因组学在内的多个应用领域。随后对解决方案进行分类，并描述了常用方法及效率指标。最后，我们指出现存挑战，并探讨了使可验证隐私保护计算更安全、更高效且更适用于实际场景的未来研究方向。