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Foundations and Trends® in Privacy and Security
Article . 2022 . Peer-reviewed
Data sources: Crossref
DBLP
Article . 2022
Data sources: DBLP
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Proofs, Arguments, and Zero-Knowledge

Authors: Justin Thaler;

Proofs, Arguments, and Zero-Knowledge

Abstract

Interactive proofs (IPs) and arguments are cryptographic protocols that enable an untrusted prover to provide a guarantee that it performed a requested computation correctly. Introduced in the 1980s, IPs and arguments represented a major conceptual expansion of what constitutes a “proof” that a statement is true. Traditionally, a proof is a static object that can be easily checked step-by-step for correctness. In contrast, IPs allow for interaction between prover and verifier, as well as a tiny but nonzero probability that an invalid proof passes verification. Arguments (but not IPs) even permit there to be “proofs” of false statements, so long as those “proofs” require exorbitant computational power to find. To an extent, these notions mimic in-person interactions that mathematicians use to convince each other that a claim is true, without going through the painstaking process of writing out and checking a traditional static proof. Celebrated theoretical results from the 1980s and 1990s such as IP = PSPACE and MIP = NEXP showed that, in principle, surprisingly complicated statements can be verified efficiently. What is more, any argument can in principle be transformed into one that is zero-knowledge, which means that proofs reveal no information other than their own validity. Zero-knowledge arguments have a myriad of applications in cryptography. Within the last decade, general-purpose zero-knowledge arguments have made the jump from theory to practice. This has opened new doors in the design of cryptographic systems, and generated additional insights into the power of IPs and arguments (zero-knowledge or otherwise). There are now no fewer than five promising approaches to designing efficient, general-purpose zero-knowledge arguments. This survey covers these approaches in a unified manner, emphasizing commonalities between them.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
44
Top 1%
Top 10%
Top 1%
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