LIPIcs.STACS.2020.21.pdf
- Filesize: 438 kB
- 12 pages
Document
Secret Key Agreement from Correlated Data, with No Prior Information
Author
-
Part of:
Volume:
37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2020-03-04
File
Document Identifiers
Acknowledgements
I want to thank Andrei Romashchenko for useful discussions. I also thank the anonymous referees for their observations which have helped me correct some errors and improve the presentation.
Cite As Get BibTex
Marius Zimand. Secret Key Agreement from Correlated Data, with No Prior Information. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.STACS.2020.21
Abstract
A fundamental question that has been studied in cryptography and in information theory is whether two parties can communicate confidentially using exclusively an open channel. We consider the model in which the two parties hold inputs that are correlated in a certain sense. This model has been studied extensively in information theory, and communication protocols have been designed which exploit the correlation to extract from the inputs a shared secret key. However, all the existing protocols are not universal in the sense that they require that the two parties also know some attributes of the correlation. In other words, they require that each party knows something about the other party’s input. We present a protocol that does not require any prior additional information. It uses space-bounded Kolmogorov complexity to measure correlation and it allows the two legal parties to obtain a common key that looks random to an eavesdropper that observes the communication and is restricted to use a bounded amount of space for the attack. Thus the protocol achieves complexity-theoretical security, but it does not use any unproven result from computational complexity. On the negative side, the protocol is not efficient in the sense that the computation of the two legal parties uses more space than the space allowed to the adversary.
Subject Classification
ACM Subject Classification
- Theory of computation → Models of computation
- Mathematics of computing → Information theory
- Security and privacy → Information-theoretic techniques
Keywords
- secret key agreement
- Kolmogorov complexity
- extractors
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
- Rudolf Ahlswede and Imre Csiszár. Common randomness in information theory and cryptography - I: secret sharing. IEEE Trans. Information Theory, 39(4):1121-1132, 1993. URL: https://doi.org/10.1109/18.243431.
- Bruno Bauwens and Marius Zimand. Linear list-approximation for short programs (or the power of a few random bits). In IEEE 29th Conference on Computational Complexity, CCC 2014, Vancouver, BC, Canada, June 11-13, 2014, pages 241-247. IEEE, 2014. URL: https://doi.org/10.1109/CCC.2014.32.
-
Charles H. Bennett, Gilles Brassard, and Jean-Marc Robert. Privacy amplification by public discussion. SIAM Journal on Computing, 17(2):210-229, 1988.
- Mark Braverman and Anup Rao. Information equals amortized communication. In Rafail Ostrovsky, editor, IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, USA, October 22-25, 2011, pages 748-757. IEEE Computer Society, 2011. URL: https://doi.org/10.1109/FOCS.2011.86.
- Harry Buhrman, Michal Koucký, and Nikolai K. Vereshchagin. Randomised individual communication complexity. In Proceedings of the 23rd Annual IEEE Conference on Computational Complexity, CCC 2008, 23-26 June 2008, College Park, Maryland, USA, pages 321-331. IEEE Computer Society, 2008. URL: https://doi.org/10.1109/CCC.2008.33.
- Alexander Kozachinskiy. On Slepian-Wolf theorem with interaction. Theory Comput. Syst., 62(3):583-599, 2018. URL: https://doi.org/10.1007/s00224-016-9741-x.
-
Sik Kow Leung-Yan-Cheong. Multi-user and wiretap channels including feedback, July 1976. Tech. Rep. No. 6603-2, Stanford Univ.
- Ueli M. Maurer. Secret key agreement by public discussion from common information. IEEE Trans. Information Theory, 39(3):733-742, 1993. URL: https://doi.org/10.1109/18.256484.
- Andrei A. Muchnik. Conditional complexity and codes. Theor. Comput. Sci., 271(1-2):97-109, 2002. URL: https://doi.org/10.1016/S0304-3975(01)00033-0.
- D. Musatov, A. E. Romashchenko, and A. Shen. Variations on Muchnik’s conditional complexity theorem. Theory Comput. Syst., 49(2):227-245, 2011. URL: https://doi.org/10.1007/s00224-011-9321-z.
- Prakash Narayan and Himanshu Tyagi. Multiterminal secrecy by public discussion. Foundations and Trends in Communications and Information Theory, 13(2-3):129-275, 2016. URL: https://doi.org/10.1561/0100000072.
- Ran Raz, Omer Reingold, and Salil P. Vadhan. Extracting all the randomness and reducing the error in Trevisan’s extractors. J. Comput. Syst. Sci., 65(1):97-128, 2002. URL: https://doi.org/10.1006/jcss.2002.1824.
-
Andrei E. Romashchenko and Marius Zimand. An operational characterization of mutual information in algorithmic information theory. In 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, July 9-13, 2018, Prague, Czech Republic, pages 95:1-95:14, 2018.
- Salil P. Vadhan. Pseudorandomness. Foundations and Trends in Theoretical Computer Science, 7(1-3):1-336, 2012. URL: https://doi.org/10.1561/0400000010.
- Marius Zimand. Kolmogorov complexity version of Slepian-Wolf coding. In Hamed Hatami, Pierre McKenzie, and Valerie King, editors, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, June 19-23, 2017, pages 22-32. ACM, 2017. URL: https://doi.org/10.1145/3055399.3055421.