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

## TL;DR

This paper establishes an inequality linking the probability of correctly estimating a discrete variable from correlated data to the mutual information, with implications for cryptographic security analysis.

## Contribution

It introduces a new inequality connecting estimation success probability and mutual information, aiding security evaluations in cryptography.

## Key findings

- Derived an inequality relating estimation probability and mutual information.
- Provides insights into the secrecy exponent in strong secrecy criteria.
- Useful for analyzing security in cryptographic systems.

## Abstract

Let $X$, $Y$ be two correlated discrete random variables. We consider an estimation of $X$ from encoded data $\varphi(Y)$ of $Y$ by some encoder function $\varphi(Y)$. We derive an inequality describing a relation of the correct probability of estimation and the mutual information between $X$ and $\varphi(Y)$. 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.