Abstract
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 language | English |
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Title of host publication | Public-Key Cryptography – PKC 2023 - 26th IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings |
Editors | Alexandra Boldyreva, Vladimir Kolesnikov |
Publisher | Springer Science and Business Media Deutschland GmbH |
Pages | 127-158 |
Number of pages | 32 |
ISBN (Print) | 9783031313707 |
DOIs | |
State | Published - 2023 |
Event | 26th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2023 - Atlanta, United States Duration: 7 May 2023 → 10 May 2023 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 13941 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 26th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2023 |
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Country/Territory | United States |
City | Atlanta |
Period | 7/05/23 → 10/05/23 |
Bibliographical note
Publisher Copyright:© 2023, International Association for Cryptologic Research.