Classical Analog to Entanglement Reversibility

In this Letter we study the problem of secrecy reversibility. This asks when two honest parties can distill secret bits from some tripartite distribution p_XYZ and transform secret bits back into p_XYZ at equal rates using local operation and public communication. This is the classical analog to the well-studied problem of reversibly concentrating and diluting entanglement in a quantum state. We identify the structure of distributions possessing reversible secrecy when one of the honest parties holds a binary distribution, and it is possible that all reversible distributions have this form. These distributions are more general than what is obtained by simply constructing a classical analog to the family of quantum states known to have reversible entanglement. An indispensable tool used in our analysis is a conditional form of the Gács-Körner common information.