Transmission, Identification and Common Randomness Capacities for Wire-Tape Channels with Secure Feedback from the Decoder

  • R. Ahlswede
  • N. Cai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)


We analyze wire-tape channels with secure feedback from the legitimate receiver. We present a lower bound on the transmission capacity (Theorem 1), which we conjecture to be tight and which is proved to be tight (Corollary 1) for Wyner’s original (degraded) wire-tape channel and also for the reversely degraded wire-tape channel for which the legitimate receiver gets a degraded version from the enemy (Corollary 2).

Somewhat surprisingly we completely determine the capacities of secure common randomness (Theorem 2) and secure identification (Theorem 3 and Corollary 3). Unlike for the DMC, these quantities are different here, because identification is linked to non-secure common randomness.


Transmission Capacity Secret Sharing Scheme Legal User Input Alphabet Security Criterion 
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  1. 1.
    Ahlswede, R.: Universal coding. In: The 7th Hawai International Conference on System Science (January 1974); Published in [A21]Google Scholar
  2. 2.
    Ahlswede, R.: Coloring hypergraphs: A new approach to multi-user source coding, Part I. J. Comb. Inform. Syst. Sci. 4(1), 76–115 (1979); Part II 5(3), 220–268 (1980)Google Scholar
  3. 3.
    Ahlswede, R., Csiszár, I.: Common randomness in information theory and cryptography, Part I: Secret sharing. IEEE Trans. Inf. Theory 39(4), 1121–1132 (1993); Part II: CR capacity 44(1), 55–62 (1998)Google Scholar
  4. 4.
    Ahlswede, R., Dueck, G.: Identification via channels. IEEE Trans. Inform. Theory 35(1), 15–29 (1989)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ahlswede, R., Dueck, G.: Identification in the presence of feedback – a discovery of new capacity formulas. IEEE Trans. Inform. Theory 35(1), 30–39 (1989)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ahlswede, R.: General theory of information transfer, Preprint 97–118, SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld (1997); General theory of information transfer: updated, General Theory of Information Transfer and Combinatorics, a Special Issue of Discrete Applied Mathematics (to appear)Google Scholar
  7. 7.
    Ahlswede, R., Zhang, Z.: New directions in the theory of identification via channels. IEEE Trans. Inform. Theory 41(4), 1040–1050 (1995)MATHCrossRefGoogle Scholar
  8. 8.
    Burnashev, M.: On identification capacity of infinite alphabets or continuous time. IEEE Trans. Inform. Theory 46, 2407–2414 (2000)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Cai, N., Lam, K.-Y.: On identification secret sharing scheme. Inform. and Comp. 184, 298–310 (2002)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Csiszár, I.: Almost independence and secrecy capacity. Probl. Inform. Trans. 32, 40–47 (1996)Google Scholar
  11. 11.
    Csiszár, I., Körner, J.: Broadcast channel with confidential message. IEEE Trans. Inform. Theory 24, 339–348 (1978)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Csiszár, I., Narayan, P.: Common randomness and secret key generation with a helper. IEEE Trans. Inform. Theory 46(2), 344–366 (2000)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Shannon, C.E.: A mathematical theory of communication. Bell. Sys. Tech. J. 27, 379–423 (1948)MATHMathSciNetGoogle Scholar
  14. 14.
    Steinberg, Y.: New converses in the theory of identification via channels. IEEE Trans. Inform. Theory 44, 984–998 (1998)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Venkatesh, S., Anantharam, V.: The common randomness capacity of a network of discrete memoryless channels. IEEE Trans. Inform. Theory 46, 367–387 (2000)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Wyner, A.D.: The wiretape channel. Bell. Sys. Tech. J. 54, 1355–1387 (1975)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. Ahlswede
    • 1
  • N. Cai
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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