Perfect Secrecy in the Wild: A Characterization

Costas Cavounidis, Massimiliano Furlan and Alkis Georgiadis-Harris

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Abstract: Alice wishes to reveal the state $X$ to Bob, if he knows some other information $Y$ also known to her. If Bob does not, she wishes to reveal nothing about $X$ at all. When can Alice accomplish this? We provide a simple necessary and sufficient condition on the joint distribution of $X$ and $Y$. Shannon's result on the perfect secrecy of the one-time pad follows as a special case.

Date: 2025-06
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