Private Polynomial Commitments and Applications to MPC

Rishabh Bhadauria, Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, Wenxuan Wu, Yupeng Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 157 s. The proof size is only 169 KB and the verification time is 11.8 s. 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 s. 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.

Original languageEnglish (US)
Title of host publicationPublic-Key Cryptography – PKC 2023 - 26th IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings
EditorsAlexandra Boldyreva, Vladimir Kolesnikov
Number of pages32
ISBN (Print)9783031313707
StatePublished - 2023
Externally publishedYes
Event26th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2023 - Atlanta, United States
Duration: May 7 2023May 10 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13941 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference26th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2023
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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