α-leakage by R\'{e}nyi Divergence and Sibson Mutual Information

For f̃(t) = exp(α-1/), this paper proposes a f̃-mean information gain measure. R\'{e}nyi divergence is shown to be the maximum f̃-mean information gain incurred at each elementary event y of channel output Y and Sibson mutual information is the f̃-mean of this Y-elementary information gain. Both are proposed as α-leakage measures, indicating the most information an adversary can obtain on sensitive data. It is shown that the existing α-leakage by Arimoto mutual information can be expressed as f̃-mean measures by a scaled probability. Further, Sibson mutual information is interpreted as the maximum f̃-mean information gain over all estimation decisions applied to channel output. This reveals that the exiting generalized Blahut-Arimoto method for computing R\'{e}nyi capacity (or Gallager's error exponent) in fact maximizes a f̃-mean information gain iteratively over estimation decision and channel input. This paper also derives a decomposition of f̃-mean information gain, analogous to the Sibson identity for R\'{e}nyi divergence.