Trade-Offs in Information-Theoretic Multi-party One-Way Key Agreement
We consider the following scenario involving three honest parties, Alice, Bob, and Carol, as well as an adversary, Eve. Each party has access to a single piece of information, jointly distributed according to some distribution P. Additionally, authentic public communication is possible from Alice to Carol and from Bob to Carol. Their goal is to establish two information-theoretically secret keys, one known to Alice and Carol, and one known to Bob and Carol. We derive joint bounds on the lengths of these keys. Our protocols combine distributed variants of Slepian-Wolf coding and the leftover hash lemma. The obtained bounds are expressed in terms of smooth Rényi entropies and show that these quantities are useful in this—single-serving—context as well.
KeywordsIEEE Transaction Shannon Entropy Secrecy Capacity Honest Party Decode Error
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- [BS94]Brassard, G., Salvail, L.: Secret-key reconciliation by public discussion. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 410–423. Springer, Heidelberg (1994)Google Scholar
- [Cac97]Cachin, C.: Entropy Measures and Unconditional Security in Cryptography. PhD thesis, ETH Zurich, Switzerland (1997)Google Scholar
- [DRS04]Dodis, Y., Reyzin, L., Smith, A.: Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 523–540. Springer, Heidelberg (2004)Google Scholar
- [MKM03]Muramatsu, J., Koga, H., Mukouchi, T.: On the problem of generating mutually independent random sequences. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 86(5), 1275–1284 (2003)Google Scholar
- [MW97]Maurer, U., 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)Google Scholar
- [Ren05]Renner, R.: Security of Quantum Key Distribution. PhD thesis, ETH Zurich, Switzerland (2005), http://arxiv.org/abs/quant-ph/0512258
- [RWW06]Renner, R., Wolf, S., Wullschleger, J.: The single-serving channel capacity. In: Proceedings of the IEEE International Symposium on Information Theory, ISIT 2006 (2006)Google Scholar