Linear-Map Vector Commitments and Their Practical Applications

Campanelli, Matteo; Nitulescu, Anca; Ràfols, Carla; Zacharakis, Alexandros; Zapico, Arantxa

doi:10.1007/978-3-031-22972-5_7

Cited by 9 publications

(5 citation statements)

References 21 publications

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“…Party A does not necessarily need to see the data, it just need to be persuaded that they are "extractable" from someone. Some examples are: a foundation willing to reward someone for finding a proof of the Riemann Hypothesis, or private individuals willing to reward anyone storing specific parts of Wikipedia or the Internet Archive on a decentralized network for storage (see Section 7.2 in [CFK22] for more discussion of these and other examples).…”

Section: Applications For Rational Arguments For Deterministic Comput...mentioning

confidence: 99%

How to Make Rational Arguments Practical and Extractable

Campanelli,

Ganesh,

Gennaro

2024

IACR CiC

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We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded. Rational arguments are an interesting primitive because they generally allow for very efficient protocols, and in particular sublinear verification (i.e. where the Verifier does not have to read the entire input). In this paper we aim at narrowing the gap between literature on rational schemes and real world applications. Our contribution is two-fold. We provide the first construction of rational arguments for the class of polynomial computations that is practical (i.e., it can be applied to real-world computations on reasonably common hardware) and with logarithmic communication. Techniques-wise, we obtain this result through a compiler from information-theoretic protocols and rational proofs for polynomial evaluation. The latter could be of independent interest. As a second contribution, we propose a new notion of extractability for rational arguments. Through this notion we can obtain arguments where knowledge of a witness is incentivized (rather than incentivizing mere soundness). We show how our aforementioned compiler can also be applied to obtain efficient extractable rational arguments for N P .

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Section: Applications For Rational Arguments For Deterministic Comput...mentioning

confidence: 99%

How to Make Rational Arguments Practical and Extractable

Campanelli,

Ganesh,

Gennaro

2024

IACR CiC

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“…There have been a few different constructions of LMC and variants/extensions recently proposed in the literature [10], [12], [14], [11], [13]. The LMC in [10] is based on a ring and may not work immediately with a linear PIR scheme, which is often based on a finite field.…”

Section: Definition 9 (Linear Map Commitmentsmentioning

confidence: 99%

“…Others constructions of LMC bring in different trade-offs, e.g. no trusted setup but log-size commitment/witness, and additional properties [10,11,13].…”

Section: Definition 9 (Linear Map Commitmentsmentioning

confidence: 99%

“…We address the aforementioned drawback of the hash-based solution by using linear map commitments with a constant-size commitment on top of linear PIR schemes to provide verifiability. A linear map commitment (LMC) [10,11,12,13] allows the prover to generate a commitment C(x) to a vector x = (x 1 , x 2 , . .…”

Section: Introductionmentioning

confidence: 99%

“…We want to highlight another advantage of LMCs as the primitive for the committed PIR: as more advanced LMCs are developed, new features will be automatically added to the proposed scheme with no modifications to the underlying PIR schemes. For example, the LMC introduced in [13] allows updatability, or the lattice-based LMC developed in [11] provides post-quantum security.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Committed Private Information Retrieval

Cao¹,

Tran²,

Dau³

et al. 2023

Preprint

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A private information retrieval (PIR) scheme allows a client to retrieve a data item xi among n items x1, x2, . . . , xn from k servers, without revealing what i is even when t < k servers collude and try to learn i. Such a PIR scheme is said to be t-private. A PIR scheme is v-verifiable if the client can verify the correctness of the retrieved xi even when v ≤ k servers collude and try to fool the client by sending manipulated data. Most of the previous works in the literature on PIR assumed that v < k, leaving the case of all-colluding servers open. We propose a generic construction that combines a linear map commitment (LMC) and an arbitrary linear PIR scheme to produce a k-verifiable PIR scheme, termed a committed PIR scheme. Such a scheme guarantees that even in the worst scenario, when all servers are under the control of an attacker, although the privacy is unavoidably lost, the client won't be fooled into accepting an incorrect xi. We demonstrate the practicality of our proposal by implementing the committed PIR schemes based on the Lai-Malavolta LMC and three well-known PIR schemes using the GMP library and blst, the current fastest C library for elliptic curve pairings.

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Algebraic Reductions of Knowledge

Kothapalli

Parno

2023

Lecture Notes in Computer Science

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Linear-Map Vector Commitments and Their Practical Applications

Cited by 9 publications

References 21 publications

How to Make Rational Arguments Practical and Extractable

How to Make Rational Arguments Practical and Extractable

Committed Private Information Retrieval

Algebraic Reductions of Knowledge

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