Perfect message authentication codes are robust to small deviations from uniform key distributions

TL;DR

This paper analyzes how small deviations from uniform key distributions affect the security of perfect message authentication codes, showing they are relatively robust to such deviations.

Contribution

It provides a simple expression quantifying security loss based on the statistical distance from uniformity, highlighting robustness of perfect MACs.

Findings

Security decreases proportionally with statistical distance from uniformity

Perfect MACs are robust to small deviations in key distribution

Derived a formula linking key distribution deviation to security reduction

Abstract

We investigate the impact of (possible) deviations of the probability distribution of key values from a uniform distribution for the information-theoretic strong, or perfect, message authentication code. We found a simple expression for the decrease in security as a function of the statistical distance between the real key probability distribution and the uniform one. In a sense, a perfect message authentication code is robust to small deviations from a uniform key distribution.