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Information-Theoretic Key Agreement: From Weak to Strong Secrecy for Free

  • Ueli Maurer
  • Stefan Wolf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1807)

Abstract

One of the basic problems in cryptography is the generation of a common secret key between two parties, for instance in order to communicate privately. In this paper we consider information-theoretically secure key agreement. Wyner and subsequently Csiszár and Körner described and analyzed settings for secret-key agreement based on noisy communication channels. Maurer as well as Ahlswede and Csiszár generalized these models to a scenario based on correlated randomness and public discussion. In all these settings, the secrecy capacity and the secret-key rate, respectively, have been defined as the maximal achievable rates at which a highly-secret key can be generated by the legitimate partners. However, the privacy requirements were too weak in all these definitions, requiring only the ratio between the adversary’s information and the length of the key to be negligible, but hence tolerating her to obtain a possibly substantial amount of information about the resulting key in an absolute sense. We give natural stronger definitions of secrecy capacity and secret-key rate, requiring that the adversary obtains virtually no information about the entire key. We show that not only secret-key agreement satisfying the strong secrecy condition is possible, but even that the achievable key-generation rates are equal to the previous weak notions of secrecy capacity and secret-key rate. Hence the unsatisfactory old definitions can be completely replaced by the new ones. We prove these results by a generic reduction of strong to weak key agreement. The reduction makes use of extractors, which allow to keep the required amount of communication negligible as compared to the length of the resulting key.

Keywords

Broadcast Channel Secrecy Capacity Strong Secrecy Information Reconciliation Original Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ueli Maurer
    • 1
  • Stefan Wolf
    • 1
  1. 1.Computer Science DepartmentSwiss Federal Institute of Technology (ETH Zürich)ZürichSwitzerland

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