Abstract
We provide a simple secret-key two-party secure communication scheme, which is provably information-theoretically secure in the limited-storage-space model. The limited-storage-space model postulates an eavesdropper who can execute arbitrarily complex computations, and is only limited in the total amount of storage space (not computation space) available to him. The bound on the storage space can be arbitrarily large (e.g. terabytes), as long as it is fixed. Given this bound, the protocol guarantees that the probability of the eavesdropper of gaining any information on the message is exponentially small. The proof of our main results utilizes a novel combination of linear algebra and Kolmogorov complexity considerations.
Research supported, in part, by NSF Grant NSF-CCR-97-00365, at Harvard University.
Chapter PDF
References
Y. Aumann and U. Feige. One message proof systems with known space verifies. In D.P. Stinson, editor, Advances in Cryptology, pages 85–99. Springer-Verlag, 1993.
C. H. Bennett, G. Brassard, C. Crepeau, and U. Maurer. Generalized privacy amplification. IEEE Transactions on Information Theory, 41(6), 1995.
C. Cachin. Entropy Measures and Unconditional Security in Cryptography, volume 1. Hartung-Gorre Verlag, Konstaz, Germany, 1997.
C. Cachin and U. M. Maurer. Unconditional security against memory bounded adversaries. In Proceedings of Crypto’ 97, 1997.
A. De-Santis, G. Persiano, and M. Yung. One-message statistical zero-knowledge proofs with space-bounded verifier. In Proceedings of the 19th ICALP, 1992.
M. Li and P. M. B. Vitanyi. An Introduction to Kolmogorov Complexity and Its Applications. Springer-Verlag, New York, 2nd edition, 1997.
U. M. Maurer. Conditionally-perfect secrecy and a provably-secure randomized cipher. Journal of Cryptology, 5:53–66, 1992.
U. M. Maurer. Secret key agreement by public discussion from common information. IEEE Transactions on Information Theory, 39:733–742, 1993.
R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995.
C. E. Shannon. Communication theory of secrecy systems. Bell Systems Technical Journal, 28:656–715, 1949.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aumann, Y., Rabin, M.O. (1999). Information Theoretically Secure Communication in the Limited Storage Space Model. In: Wiener, M. (eds) Advances in Cryptology — CRYPTO’ 99. CRYPTO 1999. Lecture Notes in Computer Science, vol 1666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48405-1_5
Download citation
DOI: https://doi.org/10.1007/3-540-48405-1_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66347-8
Online ISBN: 978-3-540-48405-9
eBook Packages: Springer Book Archive