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A Short Course on Cryptography

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Hiding Data - Selected Topics

Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 12))

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Abstract

Cryptology is the science of information protection. In his pioneering paper “Communication Theory of Secrecy Systems” Claude E. Shannon (1949) investigated the following secrecy system.

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Notes

  1. 1.

    This section was written by Holger Boche and Ahmed Mansour. It is an extension of the original text of Rudolf Ahlswede, which was only a one page summary of the result of Wyner. In this text all new important developements are included. The extension of the original text was a suggestion of one of the reviewers.

References

  1. R. Ahlswede, A note on the existence of the weak capacity for channels with arbitrarily varying channel probability functions and its relation to Shannon’s zero error capacity. Ann. Math. Stat. 41(3), 1027–1033 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Ahlswede, Elimination of correlation in random codes for arbitrarily varying channels. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 44(2), 159–175 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Ahlswede, Remarks on Shannon’s secrecy systems. Probl. Control Inf. Theory 11(4), 301–318 (1982)

    MathSciNet  MATH  Google Scholar 

  4. R. Ahlswede, G. Dueck, Bad codes are good ciphers. Probl. Control Inf. Theory 11(5), 337–351 (1982)

    MathSciNet  MATH  Google Scholar 

  5. N. Alon, The Shannon capacity of a union. Combinatorica 18(3), 301–310 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. G. Bagherikaram, A.S. Motahari, A.K. Khandani, Secrecy rate region of the broadcast channel with an eavesdropper, in Proceedings of the Forty-Sixth Annual Allerton Conference (2009), pp. 834–841

    Google Scholar 

  7. I. Bjelaković, H. Boche, J. Sommerfeld, Secrecy results for compound wiretap channels. Probl. Inf. Transm. 49(1), 73–98 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. I. Bjelaković, H. Boche, J. Sommerfeld, Capacity results for arbitrarily varying wiretap channels, Information Theory, Combinatorics, and Search Theory (Springer, New York, 2013), pp. 123–144

    Chapter  Google Scholar 

  9. D. Blackwell, L. Breiman, A.J. Thomasian, The capacity of a class of channels. Ann. Math. Stat. 30(4), 1229–1241 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Bloch, J. Barros, Physical-Layer Security: From Information Theory to Security Engineering (Cambridge University Press, Cambridge, 2011)

    Book  MATH  Google Scholar 

  11. M.R. Bloch, J.N. Laneman, Strong secrecy from channel resolvability. IEEE Trans. Inf. Theory 59(12), 8077–8098 (2013)

    Article  MathSciNet  Google Scholar 

  12. H. Boche, N. Cai, J. Nötzel, The classical-quantum channel with random state parameters known to the sender, CoRR (2015). arXiv:abs/1506.06479

  13. H. Boche, R.F. Schaefer, Capacity results and super-activation for wiretap channels with active wiretappers. IEEE Trans. Inf. Forensics Secur. 8(9), 1482–1496 (2013)

    Article  Google Scholar 

  14. H. Boche, R.F. Schaefer, H.V. Poor, On the continuity of the secrecy capacity of compound and arbitrarily varying wiretap channels. IEEE Trans. Inf. Forensics Secur. 10(12), 2531–2546 (2015)

    Article  Google Scholar 

  15. Y.-K. Chia, A. El Gamal, Three-receiver broadcast channels with common and confidential messages. IEEE Trans. Inf. Theory 58(5), 2748–2765 (2012)

    Article  MathSciNet  Google Scholar 

  16. I. Csiszár, Almost independence and secrecy capacity. Probl. Peredachi Inf. 32(1), 48–57 (1996)

    MATH  Google Scholar 

  17. I. Csiszár, J. Körner, Broadcast channels with confidential messages. IEEE Trans. Inf. Theory 24(3), 339–348 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  18. I. Csiszár, J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Channels (Academic, New York, 1981)

    MATH  Google Scholar 

  19. A. El Gamal, Y.-H. Kim, Network Information Theory (Cambridge University Press, New York, 2012)

    MATH  Google Scholar 

  20. G. Giedke, M.M. Wolf, Quantum communication: super-activated hannels. Nat. Photonics 5(10), 578–580 (2011)

    Article  Google Scholar 

  21. L.H. Harper, Optimal assignments of numbers to vertices. J. Soc. Ind. Appl. Math. 12, 131–135 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  22. A.S. Holevo, Bounds for the quantity of information transmitted by a quantum communication channel. Probl. Inf. Transm. 9(3), 177–183 (1973)

    Google Scholar 

  23. A.S. Holevo, The capacity of the quantum channel with general signal states. IEEE Trans. Inf. Theory 44(1), 269–273 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Hou, G. Kramer, Effective secrecy: reliability, confusion and stealth, in Proceedings of the IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA (2014), pp. 601–605

    Google Scholar 

  25. D. Kahn, The Codebreakers - The Story of Secret Writing (MacMillan Publishing Co, New York, 1979). 9th printing

    Google Scholar 

  26. J. Körner, K. Marton, General broadcast channels with degraded message sets. IEEE Trans. Inf. Theory 23(1), 60–64 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  27. Y. Liang, G. Kramer, H.V. Poor, S.S. (Shitz), Compound wiretap channels. EURASIP J. Wirel. Commun. Netw. 2009(1), 1–12 (2009)

    Article  Google Scholar 

  28. A.S. Mansour, R.F. Schaefer, H. Boche, Joint and individual secrecy in broadcast channels with receiver side information, in IEEE 15th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Toronto, Canada (2014), pp. 369–373

    Google Scholar 

  29. A.S. Mansour, R.F. Schaefer, H. Boche, The individual secrecy capacity of degraded multi-receiver wiretap broadcast channels, in Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, United Kingdom (2015)

    Google Scholar 

  30. K. Marton, A coding theorem for the discrete memoryless broadcast channel. IEEE Trans. Inf. Theory 25(3), 306–311 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  31. U. Maurer, S. Wolf, Information-theoretic key agreement: from weak to strong secrecy for free, Advances in Cryptology — EUROCRYPT 2000, Lecture Notes in Computer Science (Springer, Berlin, 2000), pp. 351–368

    Chapter  Google Scholar 

  32. J. Nötzel, M. Wiese, H. Boche, The arbitrarily varying wiretap channel - secret randomness, stability and super-activation, in Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT) (2015), pp. 2151–2155

    Google Scholar 

  33. J. Nötzel, M. Wiese, H. Boche, The arbitrarily varying wiretap channel - deterministic and correlated random coding capacities under the strong secrecy criterion, in Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT) (2015)

    Google Scholar 

  34. R.F. Schaefer, H. Boche, H.V. Poor, Super-activation as a unique feature of secure communication in malicious environments (2015)

    Google Scholar 

  35. C.E. Shannon, Communication theory of secrecy systems. Bell Syst. Tech. J. 28, 656–715 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  36. C.E. Shannon, The zero error capacity of a noisy channel. IRE Trans. Inf. Theory 2(3), 8–19 (1956)

    Article  MathSciNet  Google Scholar 

  37. A.D. Wyner, The wire-tap channel. Bell Syst. Tech. J. 54(8), 1355–1387 (1975)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bielefeld, Bielefeld, Germany

    Rudolf Ahlswede

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  1. Rudolf Ahlswede
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Correspondence to Rudolf Ahlswede .

Editor information

Editors and Affiliations

  1. Bielefeld, Germany

    Alexander Ahlswede

  2. Faculty of Mathematics and Computer Scie, Friedrich-Schiller-University Jena, Jena, Germany

    Ingo Althöfer

  3. Department of Mathematics, University of Bielefeld, Bielefeld, Germany

    Christian Deppe

  4. Faculty of Business and Health, Univ of Applied Sciences Bielefeld, Bielefeld, Germany

    Ulrich Tamm

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Ahlswede, R. (2016). A Short Course on Cryptography. In: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (eds) Hiding Data - Selected Topics. Foundations in Signal Processing, Communications and Networking, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-31515-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-31515-7_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31513-3

  • Online ISBN: 978-3-319-31515-7

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