May 2020
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257 Reads
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166 Citations
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May 2020
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257 Reads
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166 Citations
November 2019
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216 Reads
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244 Citations
Ever since their introduction, zero-knowledge proofs have become an important tool for addressing privacy and scalability concerns in a variety of applications. In many systems each client downloads and verifies every new proof, and so proofs must be small and cheap to verify. The most practical schemes require either a trusted setup, as in (pre-processing) zk-SNARKs, or verification complexity that scales linearly with the complexity of the relation, as in Bulletproofs. The structured reference strings required by most zk-SNARK schemes can be constructed with multi-party computation protocols, but the resulting parameters are specific to an individual relation. Groth et al. discovered a zk-SNARK protocol with a universal structured reference string that is also updatable, but the string scales quadratically in the size of the supported relations. Here we describe a zero-knowledge SNARK, Sonic, which supports a universal and continually updatable structured reference string that scales linearly in size. We also describe a generally useful technique in which untrusted "helpers" can compute advice that allows batches of proofs to be verified more efficiently. Sonic proofs are constant size, and in the "helped" batch verification context the marginal cost of verification is comparable with the most efficient SNARKs in the literature.
January 2019
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36 Reads
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50 Citations
Lecture Notes in Computer Science
Recent efficient constructions of zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs), require a setup phase in which a common-reference string (CRS) with a certain structure is generated. This CRS is sometimes referred to as the public parameters of the system, and is used for constructing and verifying proofs. A drawback of these constructions is that whomever runs the setup phase subsequently possesses trapdoor information enabling them to produce fraudulent pseudoproofs.
... This valuable property makes zk-SNARK a powerful cryptographic primitive, enabling the verification of computation correctness without exposing private inputs. In the past several years, a surge of groundbreaking scientific achievements has emerged across zk-SNARK applications, including but not limited to financial services like blockchain payments [6][7][8], smart contract [9,10], and other academic areas like machine learning [11,12], multiparty computation [13][14][15] and post-quantum cryptography [16,17]. The zk-SNARK also has a promising market outlook. ...
May 2020
... The bilinear pairing is one of the techniques used for constructing zk-SNARKs. It is used in schemes such as Groth16 [1], Plonk [2] and Sonic [6]. In modern cryptography, the groups used for DLP-based zk-SNARKs are typically cyclic subgroups of groups defined via elliptic curves over finite fields, or the multiplicative group of integers modulo a very large prime p. ...
November 2019
... Let us now briefly recall from [1,8,9,10,11,12,13], the preliminary concepts of Blockchain Technology, Decentralized File System, and Zero-Knowledge Protocol, which we will often refer to throughout the paper. ...
January 2019
Lecture Notes in Computer Science