Proofs for Inner Pairing Products and Applications

Bünz, Benedikt; Maller, Mary; Mishra, Pratyush; Tyagi, Nirvan; Vesely, Psi

doi:10.1007/978-3-030-92078-4_3

Cited by 35 publications

(21 citation statements)

References 37 publications

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“…While for a small number of parties, our protocol is slower, the total running time essentially remains the same when the number of parties increases. For instance, our experiments show that our scheme takes 9,141 s for 1000 parties and 2 16 elements per party. Prior works cannot run at this scale.…”

Section: Scalable Multi-party Private Set-intersection (Mpsi)mentioning

confidence: 94%

“…Our contribution includes two flavors of private polynomial commitments with a hidden (encrypted) polynomial; one where the evaluation points are public and the other where they are private. Our schemes are built on the recent scheme of an inner product argument [16], which generalizes the inner product argument from [14] to bilinear groups. Specifically, we embed the ciphertexts encrypting the coefficients in the base group using an Additively Homomorphic Encryption (AHE) scheme introduced in [13].…”

Section: Our Contributionsmentioning

confidence: 99%

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Private Polynomial Commitments and Applications to MPC

Bhadauria

Hazay

Venkitasubramaniam

et al. 2023

Lecture Notes in Computer Science

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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.

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Section: Scalable Multi-party Private Set-intersection (Mpsi)mentioning

confidence: 94%

Section: Our Contributionsmentioning

confidence: 99%

Private Polynomial Commitments and Applications to MPC

Bhadauria

Hazay

Venkitasubramaniam

et al. 2023

Lecture Notes in Computer Science

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“…: In our work, we adopt proof aggregation technique. Inspired by SnarkPack [50] [51], we resort to utilize special structure of proof to aggregate multiple proof. SnarkPack propose an approach to reduce the overhead in communication and verification time for verify multiple proofs without the need of further larger trusted setup ceremonies.…”

Section: Concrete Designmentioning

confidence: 99%

“…And then we will check that Z AB , Z C are consistent with the initial proof triples. Here we use two notions: the target inner pairing product (TIPP) and the multiexponentiation inner product (MIPP) (detail can see [50]).…”

Section: Concrete Designmentioning

confidence: 99%

Privacy-Preserving and Trustless Verifiable Fairness Audit of Machine Learning Models

Gui¹,

Tan²,

Cai³

2023

IJACSA

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In the big data era, machine learning has developed prominently and is widely used in real-world systems. Yet, machine learning raises fairness concerns, which incurs discrimination against groups determined by sensitive attributes such as gender and race. Many researchers have focused on developing fairness audit technique of machine learning model that enable users to protect themselves from discrimination. Existing solutions, however, rely on additional external trust assumptions, either on third-party entities or external components, that significantly lower the security. In this study, we propose a trustless verifiable fairness audit framework that assesses the fairness of ML algorithms while addressing potential security issues such as data privacy, model secrecy, and trustworthiness. With succinctness and non-interactive of zero knowledge proof, our framework not only guarantees audit integrity, but also clearly enhance security, enabling fair ML models to be publicly auditable and any client to verify audit results without extra trust assumption. Our evaluation on various machine learning models and real-world datasets shows that our framework achieves practical performance.

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“…These commitments are binding, but not hiding. Note that vector commitments with the properties listed below can be provided by Merkle trees [58] (see Appendix A), by algebraic techniques [12,20,23,25,42,47,51,52,70,71], or by polynomial commitments (introduced in [44]; see, e.g., [13,19] for an overview) adapted to vectors per [42, Appx. C].…”

Section: A Vector Commitmentsmentioning

confidence: 99%

Compact Certificates of Collective Knowledge

Micali¹,

Reyzin

Vlachos

et al. 2021

2021 IEEE Symposium on Security and Privacy (SP)

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We introduce compact certificate schemes, which allow any party to take a large number of signatures on a message 𝑀, by many signers of different weights, and compress them to a much shorter certificate. This certificate convinces the verifiers that signers with sufficient total weight signed 𝑀, even though the verifier will not see-let alone verify-all of the signatures. Thus, for example, a compact certificate can be used to prove that parties who jointly have a sufficient total account balance have attested to a given block in a blockchain.After defining compact certificates, we demonstrate an efficient compact certificate scheme. We then show how to implement such a scheme in a decentralized setting over an unreliable network and in the presence of adversarial parties who wish to disrupt certificate creation. Our evaluation shows that compact certificates are 50-280× smaller and 300-4000× cheaper to verify than a natural baseline approach.

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Proofs for Inner Pairing Products and Applications

Cited by 35 publications

References 37 publications

Private Polynomial Commitments and Applications to MPC

Private Polynomial Commitments and Applications to MPC

Privacy-Preserving and Trustless Verifiable Fairness Audit of Machine Learning Models

Compact Certificates of Collective Knowledge

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