  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.

Cryptography and Security