  Aggregate statistics play an important role in extracting meaningful insights
from distributed data while preserving privacy. A growing number of application
domains, such as healthcare, utilize these statistics in advancing research and
improving patient care.
  In this work, we explore the challenge of input validation and public
verifiability within privacy-preserving aggregation protocols. We address the
scenario in which a party receives data from multiple sources and must verify
the validity of the input and correctness of the computations over this data to
third parties, such as auditors, while ensuring input data privacy. To achieve
this, we propose the "VPAS" protocol, which satisfies these requirements. Our
protocol utilizes homomorphic encryption for data privacy, and employs
Zero-Knowledge Proofs (ZKP) and a blockchain system for input validation and
public verifiability. We constructed VPAS by extending existing verifiable
encryption schemes into secure protocols that enable N clients to encrypt,
aggregate, and subsequently release the final result to a collector in a
verifiable manner.
  We implemented and experimentally evaluated VPAS with regard to encryption
costs, proof generation, and verification. The findings indicate that the
overhead associated with verifiability in our protocol is 10x lower than that
incurred by simply using conventional zkSNARKs. This enhanced efficiency makes
it feasible to apply input validation with public verifiability across a wider
range of applications or use cases that can tolerate moderate computational
overhead associated with proof generation.
