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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 adve ...
, 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 p ...
s X = \_ where I 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 number ...
) index set, and each X_i is a random variable, or probability distribution. Often I=\N and it is required that each X_n have a certain property for ''n'' sufficiently large. For example, a uniform ensemble U = \_ is a distribution ensemble where each U_n 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.


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 *
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. The ensemble X is called pseudorandom if X and U are indistinguishable in polynomial t ...
*
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 {{crypto-stub