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

Eric Chitambar, Benjamin Fortescue, Min Hsiu Hsieh

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Proceedings
EditorsMatthew Robshaw, Rosario Gennaro
Number of pages20
ISBN (Print)9783662479995
StatePublished - 2015
Externally publishedYes
Event35th Annual Cryptology Conference, CRYPTO 2015 - Santa Barbara, United States
Duration: Aug 16 2015Aug 20 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other35th Annual Cryptology Conference, CRYPTO 2015
Country/TerritoryUnited States
CitySanta Barbara


  • Gàcs-Körner Common Information
  • Information-theoretic security
  • Public key agreement

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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