The
variation distance of two distributions
and
over a finite domain
, (often referred to as ''statistical difference''
or ''statistical distance''
[
Reyzin, Leo. (Lecture Notes]
Extractors and the Leftover Hash Lemma
in cryptography) is defined as
.
We say that two
probability ensembles and
are statistically close if
is a
negligible function In mathematics, a negligible function is a function \mu:\mathbb\to\mathbb such that for every positive integer ''c'' there exists an integer ''N'c'' such that for all ''x'' > ''N'c'',
:, \mu(x), 0 such that for all ''x'' ...
in
.
References
See also
*
Zero-knowledge proof
In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information a ...
*
Randomness extractor A randomness extractor, often simply called an "extractor", is a function, which being applied to output from a weakly random entropy source, together with a short, uniformly random seed, generates a highly random output that appears independent fro ...
Cryptography
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