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In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties: a prover and a verifier. The parties interact by exchanging messages in order to ascertain whether a given string belongs to a language or not. The prover possesses unlimited computational resources but cannot be trusted, while the verifier has bounded computation power but is assumed to be always honest. Messages are sent between the verifier and prover until the verifier has an answer to the problem and has "convinced" itself that it is correct.
A commitment scheme is a cryptographic primitive that allows one to commit to a chosen value while keeping it hidden to others, with the ability to reveal the committed value later. Commitment schemes are designed so that a party cannot change the value or statement after they have committed to it: that is, commitment schemes are binding. Commitment schemes have important applications in a number of cryptographic protocols including secure coin flipping, zero-knowledge proofs, and secure computation.
In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party can prove to another party that a given statement is true, while avoiding conveying to the verifier any information beyond the mere fact of the statement's truth. The intuition underlying zero-knowledge proofs is that it is trivial to prove the possession of certain information by simply revealing it; the challenge is to prove this possession without revealing the information, or any aspect of it whatsoever.
In cryptography, a random oracle is an oracle that responds to every unique query with a (truly) random response chosen uniformly from its output domain. If a query is repeated, it responds the same way every time that query is submitted.
In computational complexity theory, an Arthur–Merlin protocol, introduced by Babai (1985), is an interactive proof system in which the verifier's coin tosses are constrained to be public. Goldwasser & Sipser (1986) proved that all (formal) languages with interactive proofs of arbitrary length with private coins also have interactive proofs with public coins.
Shafrira Goldwasser is an Israeli-American computer scientist and winner of the Turing Award in 2012. She is the RSA Professor of Electrical Engineering and Computer Science at Massachusetts Institute of Technology; a professor of mathematical sciences at the Weizmann Institute of Science, Israel; the director of the Simons Institute for the Theory of Computing at the University of California, Berkeley; and co-founder and chief scientist of Duality Technologies.
Proof of work (PoW) is a form of cryptographic proof in which one party proves to others that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with minimal effort on their part. The concept was invented by Moni Naor and Cynthia Dwork in 1993 as a way to deter denial-of-service attacks and other service abuses such as spam on a network by requiring some work from a service requester, usually meaning processing time by a computer. The term "proof of work" was first coined and formalized in a 1999 paper by Markus Jakobsson and Ari Juels.
In cryptography, a zero-knowledge password proof (ZKPP) is a type of zero-knowledge proof that allows one party to prove to another party that it knows a value of a password, without revealing anything other than the fact that it knows the password to the verifier. The term is defined in IEEE P1363.2, in reference to one of the benefits of using a password-authenticated key exchange (PAKE) protocol that is secure against off-line dictionary attacks. A ZKPP prevents any party from verifying guesses for the password without interacting with a party that knows it and, in the optimal case, provides exactly one guess in each interaction.
In cryptography, a security parameter is a way of measuring of how "hard" it is for an adversary to break a cryptographic scheme. There are two main types of security parameter: computational and statistical, often denoted by and , respectively. Roughly speaking, the computational security parameter is a measure for the input size of the computational problem on which the cryptographic scheme is based, which determines its computational complexity, whereas the statistical security parameter is a measure of the probability with which an adversary can break the scheme.
In cryptography, a verifiable random function (VRF) is a public-key pseudorandom function that provides proofs that its outputs were calculated correctly. The owner of the secret key can compute the function value as well as an associated proof for any input value. Everyone else, using the proof and the associated public key, can check that this value was indeed calculated correctly, yet this information cannot be used to find the secret key.
In cryptography, a proof of knowledge is an interactive proof in which the prover succeeds in 'convincing' a verifier that the prover knows something. What it means for a machine to 'know something' is defined in terms of computation. A machine 'knows something', if this something can be computed, given the machine as an input. As the program of the prover does not necessarily spit out the knowledge itself a machine with a different program, called the knowledge extractor is introduced to capture this idea. We are mostly interested in what can be proven by polynomial time bounded machines. In this case the set of knowledge elements is limited to a set of witnesses of some language in NP.
In cryptography, the Feige–Fiat–Shamir identification scheme is a type of parallel zero-knowledge proof developed by Uriel Feige, Amos Fiat, and Adi Shamir in 1988. Like all zero-knowledge proofs, it allows one party, the Prover, to prove to another party, the Verifier, that they possess secret information without revealing to Verifier what that secret information is. The Feige–Fiat–Shamir identification scheme, however, uses modular arithmetic and a parallel verification process that limits the number of communications between Prover and Verifier.
Non-interactive zero-knowledge proofs are cryptographic primitives, where information between a prover and a verifier can be authenticated by the prover, without revealing any of the specific information beyond the validity of the statement itself. This function of encryption makes direct communication between the prover and verifier unnecessary, effectively removing any intermediaries. The core trustless cryptography "proofing" involves a hash function generation of a random number, constrained within mathematical parameters determined by the prover and verifier.
The Password Authenticated Key Exchange by Juggling is a password-authenticated key agreement protocol, proposed by Feng Hao and Peter Ryan. This protocol allows two parties to establish private and authenticated communication solely based on their shared (low-entropy) password without requiring a Public Key Infrastructure. It provides mutual authentication to the key exchange, a feature that is lacking in the Diffie–Hellman key exchange protocol.
In cryptography, the Fiat–Shamir heuristic is a technique for taking an interactive proof of knowledge and creating a digital signature based on it. This way, some fact can be publicly proven without revealing underlying information. The technique is due to Amos Fiat and Adi Shamir (1986). For the method to work, the original interactive proof must have the property of being public-coin, i.e. verifier's random coins are made public throughout the proof protocol.
Lance Jeremy Fortnow is a computer scientist known for major results in computational complexity and interactive proof systems. He is currently Dean of the College of Computing at the Illinois Institute of Technology.
Zerocoin is a privacy protocol proposed in 2013 by Johns Hopkins University professor Matthew D. Green and his graduate students, Ian Miers and Christina Garman. It was designed as an extension to the Bitcoin protocol that would improve Bitcoin transactions' anonymity by having coin-mixing capabilities natively built into the protocol. Zerocoin is not currently compatible with Bitcoin.
Geometric cryptography is an area of cryptology where messages and ciphertexts are represented by geometric quantities such as angles or intervals and where computations are performed by ruler and compass constructions. The difficulty or impossibility of solving certain geometric problems like trisection of an angle using ruler and compass only is the basis for the various protocols in geometric cryptography. This field of study was suggested by Mike Burmester, Ronald L. Rivest and Adi Shamir in 1996. Though the cryptographic methods based on geometry have practically no real life applications, they are of use as pedagogic tools for the elucidation of other more complex cryptographic protocols. Geometric cryptography may have applications in the future once current mainstream encryption methods are made obsolete by quantum computing.
Direct Recording Electronic with Integrity and Enforced Privacy (DRE-ip) is an End-to-End (E2E) verifiable e-voting system without involving any tallying authorities, proposed by Siamak Shahandashti and Feng Hao in 2016. It improves a previous DRE-i system by using a real-time computation strategy and providing enhanced privacy. A touch-screen based prototype of the system was trialed in the Gateshead Civic Centre polling station on 2 May 2019 during the 2019 United Kingdom local elections with positive voter feedback. A proposal that includes DRE-ip as a solution for large-scale elections was ranked 3rd place in the 2016 Economist Cybersecurity Challenge jointly organized by The Economist and Kaspersky Lab.
References
- ↑ Feige, U.; Shamir, A. (1990). "Witness indistinguishable and witness hiding protocols". Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90. pp. 416–426. doi:10.1145/100216.100272. ISBN 0897913612. S2CID 11146395.
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