Scalable Zero Knowledge Via Cycles of Elliptic Curves

By Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, Madars Virza. 2014

356 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Information Systems

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Citations in the corpus

Prio: Private, Robust, and Scalable Computation of Aggregate Statistics (2017, methodology): “We optimistically estimate that each hash computation requires only 300 multiplication gates, using a subset-sum hash function [2, 17, 67, 77], and we ignore the cost of computing the Valid circuit in the SNARK.”
Geppetto: Versatile Verifiable Computation (2015, methodology): “Recently, several lines of work [9, 46, 49, 52] on veriﬁable computation [28] have combined theoretical and engineering innovations to build systems that can verify the results of general-purpose outsourced computations while making at most cryptographic assumptions.”
PhotoProof: Cryptographic Image Authentication for Any Set of Permissible Transformations (2016, methodology): “This work is also the first application-specific use of PCD (prior prototypes were either proofs-of-concept for generic computation [7], [13] or used the special case of SNARKs [3]).”
Aurora: Transparent Succinct Arguments for R1CS (2019, background): “This approach, pioneered in [50, 45, 60, 29], relied on combining certain linearly homomorphic encodings with lightweight information-theoretic tools known as linear PCPs [54, 29, 71]; this approach was refined and optimized in several works [23, 22, 40, 51, 30, 52].”
Zero-Knowledge Contingent Payments Revisited: Attacks and Payments for Services (2017, unknown): “But advances since then in zero knowledge protocols [10, 25, 29] have made this protocol feasible and indeed there is currently a publicly available implementation of ZKCP for purchasing Sudoku solutions.”
Formalizing Human Ingenuity: A Quantitative Framework for Copyright Law's Substantial Similarity (2022, methodology): “Furthermore, using incrementally-verifiable computation [12, 13, 94], the time to produce the proofs is linear in running time of P and R.”
Verifiable Delay Functions (2018, methodology): “[11] showed an efficient construction for IVC using “cycles of Elliptic curves”.”
Spartan: Efficient and general-purpose zkSNARKs without trusted setup (2020, background): “Furthermore, unlike a vRAM-based solution, most of the non-deterministic witness needed by the circuit can be created by PC.Commit (i.e., by the Encode algorithm in computation commitments).”
Efficient RAM and control flow in verifiable outsourced computation (2015, background): “Recent work [18] has combined BCTV with theoretical foun-”
Doubly-Efficient zkSNARKs Without Trusted Setup (2018, methodology): “proof (PCP)3 and ZK transform that form the basis of many recent zkSNARK implementations [4, 5, 12, 13, 15, 16, 29, 34, 36, 39, 42–44, 64, 76, 79, 105], including systems deployed in applications like ZCash [12, 107].”
Verifiable ASICs (2016, background): “The second category includes arguments: interactive arguments with preprocessing [99–101] and non-interactive arguments with preprocessing [24, 32, 36, 61, 76, 88].”
Computational Integrity with a Public Random String from Quasi-Linear PCPs (2017, methodology): “Table 1: Quantitative comparison of SCI with KOE-based [15], IVC-based [18] and DLP-based [48] solutions.”
Full Accounting for Verifiable Outsourcing (2017, background): “Another line of work uses argument protocols, both interactive [73–75] and non-interactive [14, 21, 26, 47, 56, 66] (“SNARK” refers to the latter).”
Scalable, transparent, and post-quantum secure computational integrity (2018, methodology): “[23] Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, and Madars Virza.”
Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updatable Structured Reference Strings (2019, methodology): “Using knowledge assumptions, it is possible to build zk-SNARKs [15, 18, 35, 45, 47, 54, 59].”
Libra: Succinct Zero-Knowledge Proofs with Optimal Prover Computation (2019, background): “[26] introduced quadratic arithmetic programs (QAPs), which forms the basis of most recent implementations [11,14,19,23,25,40,46] including libSNARK [13].”
Scalable Zero Knowledge with No Trusted Setup (2019, methodology): “…by Valiant [77] (cf. [34, 28]) reduces prover space consumption by relying on knowledge extraction assumptions; this approach can be applied on top of other proof systems with succinct (sub-linear) veriﬁers, including ZK-STARK , but thus far has been realized only for a single hPKC system [23].”