Distribution ensemble

In cryptography, a distribution ensemble or probability ensemble is a family of distributions or random variables ${\displaystyle X=\{X_{i}\}_{i\in I}}${\displaystyle X=\{X_{i}\}_{i\in I}} where ${\displaystyle I}${\displaystyle I} is a (countable) index set, and each ${\displaystyle X_{i}}${\displaystyle X_{i}} is a random variable, or probability distribution. Often ${\displaystyle I=\mathbb {N} }${\displaystyle I=\mathbb {N} } and it is required that each ${\displaystyle X_{n}}${\displaystyle X_{n}} have a certain property for n sufficiently large.

For example, a uniform ensemble ${\displaystyle U=\{U_{n}\}_{n\in \mathbb {N} }}${\displaystyle U=\{U_{n}\}_{n\in \mathbb {N} }} is a distribution ensemble where each ${\displaystyle U_{n}}${\displaystyle 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.

• Provable security
• Statistically close
• Pseudorandom ensemble
• Computational indistinguishability

• Goldreich, Oded (2001). Foundations of Cryptography: Volume 1, Basic Tools. Cambridge University Press. ISBN 0-521-79172-3. Fragments available at the author's web site.

• Theory of cryptography
• Cryptography stubs

• Articles needing additional references from April 2024
• All articles needing additional references
• All stub articles