A tunable measure for information leakage called maximal -leakage is introduced. This measure quantifies the maximal gain of an adversary in refining a tilted version of its prior belief of any (potentially random) function of a dataset
conditioned on a disclosed dataset. The choice of alpa determines
the specific adversarial action ranging from refining a belief for
alpha = 1 to guessing the best posterior for alpha  = infty, and for these
extremal values this measure simplifies to mutual information
(MI) and maximal leakage (MaxL), respectively. For alpha between these extrema,
 this measure is shown to be the Arimoto channel capacity.
Several properties of this measure are proven including: (i) quasiconvexity
in the mapping between the original and disclosed
datasets; (ii) data processing inequalities; and (iii) a composition
property.

Joint work with Jiachun Liao, Oliver Kosut, and Flavio du pin Calmon