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This is called a "zero-knowledge proof of knowledge". However, a password is typically too small or insufficiently random to be used in many schemes for zero-knowledge proofs of knowledge. A zero-knowledge password proof is a special kind of zero-knowledge proof of knowledge that addresses the limited size of passwords. [citation needed]
A mathematical proof is a deductive argument for a ... where a and b are non-zero integers with no common factor. Thus, = ... Zero-knowledge proof; References
Zero knowledge may mean: Zero-knowledge proof , a concept from cryptography, an interactive method for one party to prove to another that a (usually mathematical) statement is true, without revealing anything other than the veracity of the statement
One particular motivating example is the use of commitment schemes in zero-knowledge proofs.Commitments are used in zero-knowledge proofs for two main purposes: first, to allow the prover to participate in "cut and choose" proofs where the verifier will be presented with a choice of what to learn, and the prover will reveal only what corresponds to the verifier's choice.
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 (as is the case for zero-knowledge proofs [1]) a machine with a different
Most non-interactive zero-knowledge proofs are based on mathematical constructs like elliptic curve cryptography or pairing-based cryptography, which allow for the creation of short and easily verifiable proofs of the truth of a statement. Unlike interactive zero-knowledge proofs, which require multiple rounds of interaction between the prover ...
A very useful interactive proof system is PCP(f(n), g(n)), which is a restriction of MA where Arthur can only use f(n) random bits and can only examine g(n) bits of the proof certificate sent by Merlin (essentially using random access). There are a number of easy-to-prove results about various PCP classes.
Bertrand's postulate and a proof; Estimation of covariance matrices; Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational