Statistical close

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Let the statistical difference^[1] between two distributions $X$ and $Y$ be defined as

$\Delta(X,Y)=\frac{1}{2} \sum _a | \Pr[X=\alpha] - \Pr[Y=\alpha] |$ .

We say that two probability ensembles $\{X_k\}_{k\in\N}$ and $\{Y_k\}_{k\in\N}$ are statistical close if $Δ(X k, Y k)$ is a negligible function in $k$ .

Statistical difference is based on the L1_norm.

[edit] References

^ Amit Sahai, Salil P. Vadhan: A complete problem for statistical zero knowledge. J. ACM 50(2): 196-249 (2003)

[edit] See also

Zero-knowledge proof

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