In
cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...
, a distribution ensemble or probability ensemble is a family of distributions or
random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
s
where
is a (
countable
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers; ...
) index set, and each
is a random variable, or probability distribution. Often
and it is required that each
have a certain property for ''n'' sufficiently large.
For example, a uniform ensemble
is a distribution ensemble where each
is
uniformly distributed over strings of length ''n''. In fact, many applications of probability ensembles implicitly assume that the probability spaces for the random variables all coincide in this way, so every probability ensemble is also a
stochastic process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
.
See also
*
Provable security
Provable security refers to any type or level of computer security that can be proved. It is used in different ways by different fields.
Usually, this refers to mathematical proofs, which are common in cryptography. In such a proof, the capabiliti ...
*
Statistically close The variation distance of two distributions X and Y over a finite domain D, (often referred to as ''statistical difference''
or ''statistical distance''
Reyzin, Leo. (Lecture NotesExtractors and the Leftover Hash Lemma in cryptography) is define ...
*
Pseudorandom ensemble
In cryptography, a pseudorandom ensemble is a family of variables meeting the following criteria:
Let U = \_ be a uniform ensemble
and X = \_ be an ensemble
Ensemble may refer to:
Art
* Architectural ensemble
* ''Ensemble'' (album), Kendji ...
*
Computational indistinguishability
In computational complexity and cryptography, two families of distributions are computationally indistinguishable if no efficient algorithm can tell the difference between them except with negligible probability.
Formal definition
Let \scriptstyle ...
References
* Goldreich, Oded (2001). ''Foundations of Cryptography: Volume 1, Basic Tools''. Cambridge University Press. . Fragments available at th
author's web site
Theory of cryptography
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