Paper 2023/680

Private Polynomial Commitments and Applications to MPC

Rishabh Bhadauria, Bar-Ilan University
Carmit Hazay, Bar-Ilan University, Ligero Inc
Muthuramakrishnan Venkitasubramaniam, Georgetown University, Ligero Inc
Wenxuan Wu, Texas A&M University
Yupeng Zhang, Texas A&M University

Polynomial commitment schemes allow a prover to commit to a polynomial and later reveal the evaluation of the polynomial on an arbitrary point along with proof of validity. This object is central in the design of many cryptographic schemes such as zero-knowledge proofs and verifiable secret sharing. In the standard definition, the polynomial is known to the prover whereas the evaluation points are not private. In this paper, we put forward the notion of private polynomial commitments that capture additional privacy guarantees, where the evaluation points are hidden from the verifier while the polynomial is hidden from both. We provide concretely efficient constructions that allow simultaneously batch the verification of many evaluations with a small additive overhead. As an application, we design a new concretely efficient multi-party private set-intersection with malicious security and improved asymptotic communication and space complexities. We demonstrate the concrete efficiency of our construction via an implementation. Our scheme can prove $2^{10}$ evaluations of a private polynomial of degree $2^{10}$ in 157s. The proof size is only 169KB and the verification time is 11.8s. Moreover, we also implemented the multi-party private set intersection protocol and scale it to 1000 parties (which has not been shown before). The total running time for $2^{14}$ elements per party is 2,410 seconds. While existing protocols offer better computational complexity, our scheme offers significantly smaller communication and better scalability (in the number of parties) owing to better memory usage.

Available format(s)
Cryptographic protocols
Publication info
A minor revision of an IACR publication in PKC 2023
Polynomial CommitmentsMulti-party PSIMPC
Contact author(s)
rishabh bhadauria @ gmail com
2023-05-15: approved
2023-05-12: received
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Creative Commons Attribution


      author = {Rishabh Bhadauria and Carmit Hazay and Muthuramakrishnan Venkitasubramaniam and Wenxuan Wu and Yupeng Zhang},
      title = {Private Polynomial Commitments and Applications to MPC},
      howpublished = {Cryptology ePrint Archive, Paper 2023/680},
      year = {2023},
      doi = {10.1007/978-3-031-31371-4_5},
      note = {\url{}},
      url = {}
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