Distributions attaining secret key at a rate of the conditional mutual information

Publication Type:
Conference Proceeding
Advances in Cryptology - CRYPTO 2015: 35th Annual Cryptology Conference Santa Barbara, CA, USA, August 16–20, 2015 Proceedings, Part II, 2015, 9216 pp. 443 - 462
Issue Date:
Full metadata record
Files in This Item:
Filename Description Size
CRYPTO-Camera-Ready-Final-Page-Limit.pdfAccepted Manuscript version444.66 kB
Adobe PDF
© 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 Gàcs-Körner Common Information. We thus provide an operational interpretation of the conditional Gàcs- 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.
Please use this identifier to cite or link to this item: