SPARKs: Succinct Parallelizable Arguments of Knowledge

Ephraim, Naomi; Freitag, Cody; Komargodski, Ilan; Pass, Rafael

doi:10.1007/978-3-030-45721-1_25

Cited by 16 publications

(5 citation statements)

References 36 publications

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“…In a recent work [31], the first memory-hard VDF construction was proposed by combining a SNARK with a parallelizable prover with a memoryhard "sequential" function. Although this result is close in spirit with what a VCBF tries to achieve, we do not aim for an explicit time lower bound, whereas 1 We stress that, in the setting of memory-hard functions, the term "memory" is used to denote the number of memory blocks required to correctly evaluate (in a given time) the function.…”

Section: Minimum Number Of Memory Accessmentioning

confidence: 99%

Verifiable Capacity-Bound Functions: A New Primitive from Kolmogorov Complexity

Ateniese

Chen

Francati

et al. 2023

Lecture Notes in Computer Science

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We initiate the study of verifiable capacity-bound function (VCBF). The main VCBF property imposes a strict lower bound on the number of bits read from memory during evaluation (referred to as minimum capacity). No adversary, even with unbounded computational resources, should produce an output without spending this minimum memory capacity. Moreover, a VCBF allows for an efficient public verification process: Given a proof of correctness, checking the validity of the output takes significantly fewer memory resources, sublinear in the target minimum capacity. Finally, it achieves soundness, i.e., no computationally bounded adversary can produce a proof that passes verification for a false output. With these properties, we believe a VCBF can be viewed as a "space" analog of a verifiable delay function. We then propose the first VCBF construction relying on evaluating a degree-d polynomial f from Fp[x] at a random point. We leverage ideas from Kolmogorov complexity to prove that sampling f from a large set (i.e., for high-enough d) ensures that evaluation must entail reading a number of bits proportional to the size of its coefficients. Moreover, our construction benefits from existing verifiable polynomial evaluation schemes to realize our efficient verification requirements. In practice, for a field of order O(2 λ ) our VCBF achieves O((d + 1)λ) minimum capacity, whereas verification requires just O(λ). The minimum capacity of our VCBF construction holds against adversaries that perform a constant number of random memory accesses during evaluation. This poses the natural question of whether a VCBF with high minimum capacity guarantees exists when dealing with adversaries that perform non-constant (e.g., polynomial) number of random accesses.

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Section: Minimum Number Of Memory Accessmentioning

confidence: 99%

Verifiable Capacity-Bound Functions: A New Primitive from Kolmogorov Complexity

Ateniese

Chen

Francati

et al. 2023

Lecture Notes in Computer Science

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“…Unfortunately, avoiding such outcomes is not easy, and in this work, we seek to strengthen our security definitions to avoid such issues. We do this in two ways: unlike [24], our definitions model the unforgeability period computationally -through the widelyadopted technique of bounding the number of sequential computation steps the adversary may compute [6,16,35,36,43]. While this still requires conversion when used in the real world, it does not embed the conversion into the security definition.…”

Section: Defining Time-deniable Signaturesmentioning

confidence: 99%

“…For our time lock puzzle, we modified an existing, open-source implementation of an RSW time-lock puzzle [25]. Our timestamp supports 2 16 different values which is approximately equivalent to what is supported by [40]. This is reasonable given at least some motivating applications (i.e.…”

Section: Implementation and Evaluationmentioning

confidence: 99%

“…We begin the analysis by examining the effect of varying 𝑁 . It is an important parameter for our scheme because 𝑁 and 𝑑 must satisfy 𝑁 𝑑 > 2 16 and together determine the efficiency of signing and verifying. To be explicit, signing consists of extracting at most 𝑑 • (𝑁 − 1) keys from the HIBE tree where each key is 𝑂 (𝑑) group elements long and requires 𝑂 (𝑑) work to generate.…”

Section: Implementation and Evaluationmentioning

confidence: 99%

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Time-Deniable Signatures

Beck

Choudhuri

Green

et al. 2023

PoPETs

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In this work we propose time-deniable signatures (TDS), a new primitive that facilitates deniable authentication in protocols such as DKIM-signed email. As with traditional signatures, TDS provide strong authenticity for message content, at least {\em for a sender-chosen period of time}. Once this time period has elapsed, however, time-deniable signatures can be forged by any party who obtains a signature. This forgery property ensures that signatures serve a useful authentication purpose for a bounded time period, while also allowing signers to plausibly disavow the creation of older signed content. Most critically, and unlike many past proposals for deniable authentication, TDS do not require interaction with the receiver or the deployment of any persistent cryptographic infrastructure or services beyond the signing process ( e.g., APIs to publish secrets or author timestamp certificates.) We first investigate the security definitions for time-deniability, demonstrating that past definition attempts are insufficient (and indeed, allow for broken signature schemes.) We then propose an efficient construction of TDS based on well-studied assumptions.

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“…• SPARKs [44]: This work breaks the computation task into a sequence of smaller subtasks, and delegates the proof generation for the correctness of each sub-task to one server.…”

Section: Introductionmentioning

confidence: 99%

Multi-Party Proof Generation in QAP-based zk-SNARKs

Rahimi¹,

Maddah-Ali²

2021

Preprint

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Zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) allows a party, known as the prover, to convince another party, known as the verifier, that he knows a private value v, without revealing it, such that F (u, v) = y for some function F and public values u and y. There are various versions of zk-SNARK, among them, Quadratic Arithmetic Program (QAP)-based zk-SNARK has been widely used in practice, specially in Blockchain technology. This is attributed to two desirable features; its fixed-size proof and the very light computation load of the verifier. However, the computation load of the prover in QAP-based zkSNARKs, is very heavy, even-though it is designed to be very efficient. This load can be beyond the prover's computation power to handle, and has to be offloaded to some external servers. In the existing offloading solutions, either (i) the load of computation, offloaded to each sever, is a fraction of the prover's primary computation (e.g., DZIK), however the servers need to be trusted, (ii) the servers are not required to be trusted, but the computation complexity imposed to each one is the same as the prover's primary computation (e.g., Trinocchio). In this paper, we present a scheme, which has the benefits of both solutions. In particular, we propose a secure multi-party proof generation algorithm where the prover can delegate its task to N servers, where (i) even if a group of T ∈ N servers, T ≤ N , collude, they cannot gain any information about the secret value v, (ii) the computation complexity of each server is less than 1/(N − T ) of the prover's primary computation. The design is such that we don't lose the efficiency of the prover's algorithm in the process of delegating the tasks to external servers.

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SPARKs: Succinct Parallelizable Arguments of Knowledge

Cited by 16 publications

References 36 publications

Verifiable Capacity-Bound Functions: A New Primitive from Kolmogorov Complexity

Verifiable Capacity-Bound Functions: A New Primitive from Kolmogorov Complexity

Time-Deniable Signatures

Multi-Party Proof Generation in QAP-based zk-SNARKs

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