Optimal Equivocation in Secrecy Systems a Special Case of Distortion-based Characterization

TL;DR

This paper demonstrates that the optimal secrecy performance measured by equivocation is a special case of a more general distortion-based framework using log-loss, providing deeper insights into secrecy metrics.

Contribution

It shows that equivocation-based secrecy limits are encompassed by distortion-based metrics, justifying the causal-disclosure framework for secrecy analysis.

Findings

Equivocation limits are special cases of distortion-based performance.

Log-loss function unifies secrecy performance metrics.

Supports causal-disclosure framework for secrecy systems.

Abstract

Recent work characterizing the optimal performance of secrecy systems has made use of a distortion-like metric for partial secrecy as a replacement for the more traditional metric of equivocation. In this work we use the log-loss function to show that the optimal performance limits characterized by equivocation are, in fact, special cases of distortion-based counterparts. This observation illuminates why equivocation doesn't tell the whole story of secrecy. It also justifies the causal-disclosure framework for secrecy (past source symbols and actions revealed to the eavesdropper).