TY - GEN

T1 - Distributions attaining secret key at a rate of the conditional mutual information

AU - Chitambar, Eric

AU - Fortescue, Benjamin

AU - Hsieh, Min Hsiu

N1 - Publisher Copyright:
© International Association for Cryptologic Research 2015.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Gàcs-Körner Common Information

KW - Information-theoretic security

KW - Public key agreement

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U2 - 10.1007/978-3-662-48000-7_22

DO - 10.1007/978-3-662-48000-7_22

M3 - Conference contribution

AN - SCOPUS:84943404046

SN - 9783662479995

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 443

EP - 462

BT - Advances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Proceedings

A2 - Robshaw, Matthew

A2 - Gennaro, Rosario

PB - Springer

T2 - 35th Annual Cryptology Conference, CRYPTO 2015

Y2 - 16 August 2015 through 20 August 2015

ER -