Abstract
We consider the information-theoretic secure key distribution problem (KDP) over noisy binary symmetric channels with public discussion and in the presence of an active adversary. There are several versions of such protocols proposed by Maurer, Wolf, Renner, Dodis, Reyzin et al. We describe two new versions of KDP for the same channel model and with the use of extractors as a mean of privacy amplification but with the goal to maximize the key rate under an optimization of the protocol parameters. There are two novelties in solution of KDP: we get the extractor’s seed directly from the distributed initial strings and we prove the main results in terms of explicit estimates without the use of the uncertain symbols O, Ω, Θ. Both asymptotic and non-asymptotic cases are presented. It is shown that the extractors can be superior to conventional hashing for very large lengths of initially distributed strings.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Knill, E.: Bulding Quantum Computers, 2007 IEEE Int. Symp. on Informational Theory. IEEE Information Theory Society Newsletter 58(4), 32–35 (2008)
Shannon, C.E.: Communication theory of secrecy systems. Bell System Technical Journal 28(4), 656–715 (1949)
Hellman, M.E.: An extension of the Shannon theory approach to cryptography. IEEE Transactions on Information Theory 23(2), 289–294 (1977)
Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proc. Int. Conf. on Computers, Systems & Signal Processing (1984)
Aono, T., Higuchi, K., Ohira, T., Komiyama, B., Sasaoka, H.: Wireless secret key generation exploiting reactance-domain scalar response of multipath fading channels. IEEE Transactions on Antennas and Propagation 53(11), 3776–3784 (2005)
Yakovlev, V., Korzhik, V., Kovajkin, Y., Morales-Luna, G.: Secret Key Agreement Over Multipath Channels Exploiting a Variable-Directional Antenna. Int. Jour. Adv. Computer Science & Applications 3(1), 172–178 (2012)
Wyner, A.: Wire-tap channel concept. Bell System Technical Journal 54, 1355–1387 (1975)
Korjik, V., Yakovlev, V.: Non-asymptotic estimates for efficiency of code jamming in a wire-tap channel. Problems of Information Transmission 17, 223–22 (1981)
Korjik, V., Yakovlev, V.: Capacity of communication channel with inner random coding. Problems of Information Transmission 28, 317–325 (1992)
Bennett, C.H., Brassard, G., Crepeau, C., Maurer, U.M.: Generalized privacy amplification. IEEE Transactions on Information Theory 41(6), 1915–1923 (1995)
Maurer, U.M.: Secret key agreement by public discussion from common information. IEEE Transactions on Information Theory 39(3), 733–742 (1993)
Maurer, U.M.: Information-Theoretically Secure Secret-Key Agreement by NOT Authenticated Public Discussion. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 209–225. Springer, Heidelberg (1997)
Maurer, U.M.: Protocols for Secret Key Agreement by Public Discussion Based on Common Information. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 461–470. Springer, Heidelberg (1993)
Maurer, U.M., Wolf, S.: Privacy Amplification Secure against Active Adversaries. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 307–321. Springer, Heidelberg (1997)
Maurer, U.M., Wolf, S.: Secret-key agreement over unauthenticated public channels iii: Privacy amplification. IEEE Trans. Information Theory 49(4), 839–851 (2003)
Maurer, U.M., Wolf, S.: Towards Characterizing when Information-Theoretic Secret Key Agreement is Possible. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 196–209. Springer, Heidelberg (1996)
Korzhik, V., Yakovlev, V., Sinuk, A.: Achieveability of the Key-Capacity in a Scenario of Key Sharing by Public Discussion and in the Presence of Passive Eavesdropper. In: Gorodetsky, V., Popyack, L.J., Skormin, V.A. (eds.) MMM-ACNS 2003. LNCS, vol. 2776, pp. 308–315. Springer, Heidelberg (2003)
Korzhik, V., Yakovlev, V., Sinuk, A.: Key Distribution Protocol Based on Noisy Channel and Error Detecting Codes. In: Gorodetski, V.I., Skormin, V.A., Popyack, L.J. (eds.) MMM-ACNS 2001. LNCS, vol. 2052, pp. 242–250. Springer, Heidelberg (2001)
Yakovlev, V., Korzhik, V., Morales-Luna, G.: Key Distribution Protocols Based on Noisy Channel in Presence of Active Adversary: Conventional and New Versions with Parameter Optimization. IEEE Transaction on Information Theory 54(6), 2535–2549 (2008)
Yakovlev, V., Korzhik, V., Morales-Luna, G.: Non-asymptotic Performance Evalua-tion of Key Distribution Protocols Based on Noisy Channels in Presence of Active Adversary. In: Proc. X Spanish Meet. Cryptology and Information Security, Salamanca, pp. 63–68 (2008)
Renner, R., Wolf, S.: Unconditional Authenticity and Privacy from an Arbitrarily Weak Secret. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 78–95. Springer, Heidelberg (2003)
Renner, R., Wolf, S.: The Exact Price for Unconditionally Secure Asymmetric Cryptography. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 109–125. Springer, Heidelberg (2004)
Dodis, Y., Katz, J., Reyzin, L., Smith, A.: Robust Fuzzy Extractors and Authenticated Key Agreement from Close Secrets. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 232–250. Springer, Heidelberg (2006)
Kanukurthi, B., Reyzin, L.: Key Agreement from Close Secrets over Unsecured Channels. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 206–223. Springer, Heidelberg (2009)
Chandran, N., Kanukurthi, B., Ostrovsky, R., Reyzin, L.: Privacy amplifcation with asymptotically optimal entropy loss. Cryptology ePrint Archive (2010), http://eprint.iacr.org/2010/
Trevisan, L.: Construction of extractors using pseudo-random generator. In: Proceedings of the 31 Annual ACM Symposium on Theory of Computing, Atlanta, pp. 141–148 (1999)
Raz, R., Reingold, O., Vadhan, S.P.: Extracting all the randomness and reducing the error in trevisan’s extractors. J. Comput. Syst. Sci. 65(1), 97–128 (2002)
Korjik, V., Morales-Luna, G., Balakirsky, V.: Privacy Amplification Theorem for Noisy Main Channel. In: Davida, G.I., Frankel, Y. (eds.) ISC 2001. LNCS, vol. 2200, pp. 18–26. Springer, Heidelberg (2001)
Korjik, V., Yakovlev, V., Chesnokov, R., Morales-Luna, G.: Performance Evaluation of Keyless Authentication Based on Noisy Channel. In: International Conference of Mathematical Methods, Models and Architectures for Computer Network Security. CCIS, vol. 1, pp. 115–126 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yakovlev, V., Korzhik, V., Bakaev, M., Morales-Luna, G. (2012). Optimization of Key Distribution Protocols Based on Extractors for Noisy Channels within Active Adversaries. In: Kotenko, I., Skormin, V. (eds) Computer Network Security. MMM-ACNS 2012. Lecture Notes in Computer Science, vol 7531. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33704-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-33704-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33703-1
Online ISBN: 978-3-642-33704-8
eBook Packages: Computer ScienceComputer Science (R0)