Efficient One-Way Secret-Key Agreement and Private Channel Coding via Polarization

  • Joseph M. Renes
  • Renato Renner
  • David Sutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8269)


We introduce explicit schemes based on the polarization phenomenon for the task of secret-key agreement from common information and one-way public communication as well as for the task of private channel coding. Our protocols are distinct from previously known schemes in that they combine two practically relevant properties: they achieve the ultimate rate—defined with respect to a strong secrecy condition—and their complexity is essentially linear in the blocklength. However, we are not able to give an efficient algorithm for code construction.


One-way secret-key agreement private channel coding one-way secret-key rate secrecy capacity wiretap channel scenario more capable less noisy degraded polarization phenomenon polar codes practically efficient strongly secure 


  1. 1.
    Shannon, C.E.: Communication theory of secrecy systems. Bell System Technical Journal 28, 656–715 (1949)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Maurer, U.: Secret key agreement by public discussion from common information. IEEE Trans. on Information Theory 39, 733–742 (1993)CrossRefMATHGoogle Scholar
  3. 3.
    Wyner, A.D.: The wire-tap channel. Bell System Technical Journal 54, 1355–1387 (1975)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Csiszár, I., Körner, J.: Broadcast channels with confidential messages. IEEE Trans. on Information Theory 24, 339–348 (1978)CrossRefMATHGoogle Scholar
  5. 5.
    Arıkan, E.: Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Trans. on Information Theory 55, 3051–3073 (2009)CrossRefGoogle Scholar
  6. 6.
    Sutter, D., Renes, J.M., Dupuis, F., Renner, R.: Efficient quantum channel coding scheme requiring no preshared entanglement. In: Proc. IEEE Int. Symposium on Information Theory (to appear, 2013)Google Scholar
  7. 7.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Interscience (2006)Google Scholar
  8. 8.
    Körner, J., Marton, K.: Comparison of two noisy channels. In: Bolyai, J. (ed.) Topics in Information Theory. Colloquia Mathematica Societatis, pp. 411–424. North-Holland, The Netherlands (1977)Google Scholar
  9. 9.
    Arıkan, E.: Source polarization. In: Proc. IEEE Int. Symposium on Information Theory, pp. 899–903 (2010)Google Scholar
  10. 10.
    Şaşoğlu, E., Telatar, E., Arıkan, E.: Polarization for arbitrary discrete memoryless channels. In: Proc. Information Theory Workshop, pp. 144–148 (2009)Google Scholar
  11. 11.
    Arıkan, E., Telatar, E.: On the rate of channel polarization. In: Proc. IEEE Int. Symposium on Information Theory (2009)Google Scholar
  12. 12.
    Honda, J., Yamamoto, H.: Polar coding without alphabet extension for asymmetric channels. In: Proc. IEEE Int. Symposium on Information Theory, pp. 2147–2151 (2012)Google Scholar
  13. 13.
    Abbe, E.: Randomness and dependencies extraction via polarization. In: Information Theory and Applications Workshop (ITA), pp. 1–7 (2011)Google Scholar
  14. 14.
    Sahebi, A.G., Pradhan, S.S.: Multilevel polarization of polar codes over arbitrary discrete memoryless channels. In: 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1718–1725 (2011)Google Scholar
  15. 15.
    Maurer, U.: The strong secret key rate of discrete random triples. In: Blahut, R.E. (ed.) Communication and Cryptography, pp. 271–285. Kluwer Academic, Boston (1994)CrossRefGoogle Scholar
  16. 16.
    Maurer, U., Wolf, S.: Information-theoretic key agreement: From weak to strong secrecy for free. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 351–368. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  17. 17.
    Ahlswede, R., Csiszár, I.: Common randomness in information theory and cryptography. i. secret sharing. IEEE Trans. on Information Theory 39, 1121–1132 (1993)CrossRefMATHGoogle Scholar
  18. 18.
    Holenstein, T., Renner, R.: One-way secret-key agreement and applications to circuit polarization and immunization of public-key encryption. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 478–493. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Maurer, U., Wolf, S.: Unconditionally secure key agreement and the intrinsic conditional information. IEEE Trans. on Information Theory 45, 499–514 (1999)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Renner, R., Wolf, S.: New bounds in secret-key agreement: The gap between formation and secrecy extraction. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 562–577. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  21. 21.
    El Gamal, A., Kim, Y.H.: Network Information Theory. Cambridge University Press (2012)Google Scholar
  22. 22.
    Abbe, E.: Low complexity constructions of secret keys using polar coding. In: Proc. Information Theory Workshop (2012)Google Scholar
  23. 23.
    Chou, R.A., Bloch, M.R., Abbe, E.: Polar coding for secret-key generation (2013), http://arxiv.org/abs/1305.4746
  24. 24.
    Mahdavifar, H., Vardy, A.: Achieving the secrecy capacity of wiretap channels using polar codes. IEEE Trans. on Information Theory 57, 6428–6443 (2011)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Bellare, M., Tessaro, S., Vardy, A.: Semantic security for the wiretap channel. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 294–311. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  26. 26.
    Andersson, M., Rathi, V., Thobaben, R., Kliewer, J., Skoglund, M.: Nested polar codes for wiretap and relay channels. IEEE Communications Letters 14, 752–754 (2010)CrossRefGoogle Scholar
  27. 27.
    Hof, E., Shamai, S.: Secrecy-achieving polar-coding. In: Proc. Information Theory Workshop, pp. 1–5 (2010)Google Scholar
  28. 28.
    Koyluoglu, O.O., El Gamal, H.: Polar coding for secure transmission and key agreement. In: IEEE 21st International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), pp. 2698–2703 (2010)Google Scholar
  29. 29.
    Şaşoğlu, E., Vardy, A.: A new polar coding scheme for strong security on wiretap channels. In: Proc. IEEE Int. Symposium on Information Theory (to appear, 2013)Google Scholar
  30. 30.
    Hayashi, M., Matsumoto, R.: Construction of wiretap codes from ordinary channel codes. In: Proc. IEEE Int. Symposium on Information Theory, pp. 2538–2542 (2010)Google Scholar
  31. 31.
    Karzand, M., Telatar, E.: Polar codes for q-ary source coding. In: Proc. IEEE Int. Symposium on Information Theory, pp. 909–912 (2010)Google Scholar
  32. 32.
    Tal, I., Sharov, A., Vardy, A.: Constructing polar codes for non-binary alphabets and macs. In: Proc. IEEE Int. Symposium on Information Theory, pp. 2132–2136 (2012)Google Scholar
  33. 33.
    Tal, I., Vardy, A.: How to construct polar codes. Submitted to IEEE Transactions on Information Theory (2011), arXiv:1105.6164Google Scholar
  34. 34.
    Sutter, D., Renes, J.M., Dupuis, F., Renner, R.: Achieving the capacity of any DMC using only polar codes. In: Proc. Information Theory Workshop, pp. 114–118 (2012); extended version available at arXiv:1205.3756 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Joseph M. Renes
    • 1
  • Renato Renner
    • 1
  • David Sutter
    • 1
  1. 1.Institute for Theoretical PhyiscsETH ZurichSwitzerland

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