Definition

Suppose random variables XX and YY with support 𝒵\mathcal{Z}, then the statistical distance 𝖲𝖣\mathsf{SD} of X,YX,Y is

𝖲𝖣(X,Y)=12∑z∈𝒵|Pr⁡[X=z]−Pr⁡[Y=z]|\mathsf{SD}(X,Y) = \frac{1}{2}\sum_{z \in \mathcal{Z}} \lvert \Pr[X=z]-\Pr[Y=z]\rvert

References

  1. https://www.ccs.neu.edu/home/wichs/class/crypto-fall17/lecture3.pdf