AB - © International Association for Cryptologic Research 2015. In this paper we consider the problem of extracting secret key from an eavesdropped source pXY Z at a rate given by the conditional mutual information. We investigate this question under three different scenarios: (i) Alice (X) and Bob (Y) are unable to communicate but share common randomness with the eavesdropper Eve (Z), (ii) Alice and Bob are allowed one-way public communication, and (iii) Alice and Bob are allowed two-way public communication. Distributions having a key rate of the conditional mutual information are precisely those in which a ?helping? Eve offers Alice and Bob no greater advantage for obtaining secret key than a fully adversarial one. For each of the above scenarios, strong necessary conditions are derived on the structure of distributions attaining a secret key rate of I(X: Y |Z). In obtaining our results, we completely solve the problem of secret key distillation under scenario (i) and identify H(S|Z) to be the optimal key rate using shared randomness, where S is the Gŕcs-Körner Common Information. We thus provide an operational interpretation of the conditional Gŕcs- Körner Common Information. Additionally, we introduce simple example distributions in which the rate I(X: Y |Z) is achievable if and only if two-way communication is allowed.
AU - Chitambar, E
AU - Fortescue, B
AU - Hsieh, MH
DA - 2015/01/01
DO - 10.1007/978-3-662-48000-7_22
EP - 462
JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PY - 2015/01/01
SP - 443
TI - Distributions attaining secret key at a rate of the conditional mutual information
VL - 9216
Y1 - 2015/01/01
Y2 - 2019/06/19
ER -