On a Relationship between the Correct Probability of Estimation from Correlated Data and Mutual Information

Let X , Y be two correlated discrete random variables. We consider an estimation of X from encoded data φ(Y ) of Y by some encoder function φ(Y ). We derive an inequality describing a relation of the correct probability of estimation and the mutual information between X and φ(Y ). This inequality may be useful for the secure analysis of crypto system when we use the success probability of estimating secret data as a security criterion. It also provides an intuitive meaning of the secrecy exponent in the strong secrecy criterion.