  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 verifiable
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 37 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.
