Abstract
Techniques are presented that allow A to convince B that she knows a solution to the Discrete Log Problem—i.e. that she knows an x such that α x ≡ β (mod N) holds—without revealing anything about x to B. Protocols are given both for N prime and for N composite. We prove these protocols secure under a formal model which is of interest in its own right. We also show how A can convince B that two elements α and β generate the same subgroup in Z*N without revealing how to express either as a power of the other.
Partially supported by the Netherlands Organisation for the Advancement of Pure Research (ZWO).
partially supported by DIUC Grant #211/86.
Chapter PDF
Similar content being viewed by others
Keywords
- Polynomial Time
- Joint Probability Distribution
- Coin Flipping
- Probabilistic Polynomial Time
- Composite Number
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
R. Berger, S. Kannan, and R. Peralta, “A Framework for the Study of Cryptographic Protocols,” Proceedings of Crypto 85, (1985).
M. Blum, “Coin Flipping by Telephone,” Proc. IEEE COMPCON, pp. 133–137 (1982).
G. Brassard, and C. Crépeau, “Zero-Knowledge Simulation of Boolean Circuits,” Presented at Crypto 86, (August 1986).
D. Chaum, “Demonstrating that a Public Predicate can be Satisfied Without Revealing Any Information About How,” Presented at Crypto 86, (August 1986).
W. Diffie, and M. Hellman, “New Directions in Cryptography,” IEEE Transactions on Information Theory” IT 22, pp. 644–654 (1976).
S. Goldwasser, S. Micali, and C. Rackoff, “The Knowledge Complexity of Interactive Proof Systems,” 17th STOC (1985).
O. Goldreich, S. Micali, and A. Wigderson, “How to Prove all NP-statements in Zero-Knowledge, and a Methodology of Cryptographic Protocol Design,” Presented at Crypto 86, (August 1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chaum, D., Evertse, JH., van de Graaf, J., Peralta, R. (1987). Demonstrating Possession of a Discrete Logarithm Without Revealing it. In: Odlyzko, A.M. (eds) Advances in Cryptology — CRYPTO’ 86. CRYPTO 1986. Lecture Notes in Computer Science, vol 263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47721-7_14
Download citation
DOI: https://doi.org/10.1007/3-540-47721-7_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18047-0
Online ISBN: 978-3-540-47721-1
eBook Packages: Springer Book Archive