Abstract
In this work we investigate the power of Public Randomness in the context of Public-key cryptosystems. We consider the Diffie-Hellman Public-key model in which an additional short random string is shared by all users. This, which we call Public-Key Public-Randomness (PKPR) model, is very powerful as we show that it supports simple non-interactive implementations of important cryptographic primitives.
We give the first completely non-interactive implementation of Oblivious Transfer. Our implementation is also secure against receivers with unlimited computational power.
We propose the first implementation of non-interactive nature for Perfect Zero-Knowledge in the dual model of Brassard, Crépeau, and Chaum for all NP-languages.
Part of this work was done while the author was visiting IBM Research Division, T. J. Watson Research Ctr, Yorktown Heights, NY 10598.
Partially supported by ONR Grant #N00039-88-C-0163.
Chapter PDF
Similar content being viewed by others
Keywords
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
D. Beaver, Secure Multiparty Protocols Tolerating Half Faulty Processors, CRYPTO 1989.
M. Blum, Coin Flipping by Telephone, IEEE COMPCON 1982, pp. 133–137.
M. Blum, Three Applications of the Oblivious Transfer, Unpublished manuscript.
M. Blum, How to Prove a Theorem So No One Else Can Claim It, Proceedings of the International Congress of Mathematicians, Berkeley, California, 1986, pp. 1444–1451.
G. Brassard and C. Crépeau, Non-transitive Transfer of Confidence: A Perfect Zero-Knowledge Interactive Protocol for SAT and Beyond, Proceedings of the 27th IEEE Symp. on Foundation of Computer Science, 1986, pp. 188–195.
G. Brassard, C. Crépeau, and D. Chaum, Minimum Disclosure Proofs of Knowledge, Journal of Computer and System Sciences, vol. 37, no. 2, October 1988, pp. 156–189.
G. Brassard, C. Crépeau, and J.-M. Robert, Information Theoretic Reductions among Disclosure Problems, Proceedings of the 27th IEEE Symp. on Foundation of Computer Science, 1986, pp. 168–173.
G. Brassard, C. Crépeau, and M. Yung, Everything in NP can be Proven in Perfect Zero-Knowledge in a Bounded Number of Rounds, ICALP 89.
M. Blum, A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero Knowledge, MIT Research Report MIT/LCS/TM-430, May 1990.
M. Blum, P. Feldman, and S. Micali, Non-Interactive Zero-Knowledge Proof Systems and Applications, Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, 1988.
M. Ben-Or, S. Goldwasser, and A. Wigderson, Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computations, Proceedings of the 20th Annual ACM Symposium on Theory of Computing, 1988, pp. 1–10.
R. Boppana, J. Hastad, and S. Zachos, Does co-NP have Short Interactive Proofs?, Information Processing Letters, vol. 25, May 1987, pp. 127–132.
M. Bellare and S. Micali, Non-interactive Oblivious Transfer and Applications, CRYPTO 1989.
B. van Boer, Oblivious Transfer Protecting Secrecy, Eurocrypt 90.
D. Chaum, Demonstrating that a Public Predicate can be Satisfied Without Revealing any Information About How, in “Advances in Cryptology — CRYPTO 86”, vol. 263 of “Lecture Notes in Computer Science”, Springer Verlag, pp. 195–199.
C. Crépeau, Equivalence Between Two Flavors of Oblivious Transfer, in “Advances in Cryptology — CRYPTO 87”, vol. 293 of “Lecture Notes in Computer Science”, Springer Verlag, pp. 350–354.
D. Chaum, C. Crépeau, and I. Damgård, Multiparty Unconditionally Secure Protocols, Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, 1988, pp. 11–19.
W. Diffie and M. E. Hellman, New Directions in Cryptography, IEEE Transactions on Information Theory, vol. IT-22, no. 6, Nov. 1976, pp. 644–654.
A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero-Knowledge Proof Systems, in “Advances in Cryptology — CRYPTO 87”, vol. 293 of “Lecture Notes in Computer Science”, Springer Verlag, pp. 52–72.
A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero-Knowledge Proof-Systems with Preprocessing, in “Advances in Cryptology-CRYPTO 88”, Ed. S. Goldwasser, vol. 403 of “Lecture Notes in Computer Science”, Springer-Verlag, pp. 269–282.
A. De Santis, S. Micali, and G. Persiano, Removing Interaction from Zero-Knowledge Proofs, in “Advanced International Workshop on Sequences”, Positano, Italy, June 1988, Ed. R. M. Capocelli, Springer-Verlag, pp. 377–393.
A. De Santis and M. Yung, Cryptographic Applications of Metaproofs, CRYPTO 90.
S. Even, O. Goldreich, and A. Lempel, A Randomized Protocol for Signing Contracts, CACM, vol. 28, 1985, pp. 637–647.
L. Fortnow, The Complexity of Perfect Zero-Knowledge, Proceedings 19th Annual ACM Symposium on Theory of Computing, New York, 1987, pp. 204–209.
U. Feige, D. Lapidot, and A. Shamir, Multiple Non-Interactive Zero-Knowledge Proofs Based on a Single Random String, FOCS 90.
Z. Galil, S. Haber, and M. Yung, Cryptographic Computation: Secure Fault-Tolerant Protocols and the Public-Key Model, in “Advances in Cryptology — CRYPTO 87”, vol. 293 of “Lecture Notes in Computer Science”, Springer Verlag, pp. 135–155.
S. Goldwasser and S. Micali, Probabilistic Encryption, Journal of Computer and System Science, vol. 28, n. 2, 1984, pp. 270–299.
S. Goldwasser, S. Micali, and C. Rackoff, The Knowledge Complexity of Interactive Proof-Systems, SIAM Journal on Computing, vol. 18, n. 1, February 1989.
O. Goldreich, S. Micali, and A. Wigderson, Proofs that Yield Nothing but their Validity and a Methodology of Cryptographic Design, Proceedings of 27th Annual Symposium on Foundations of Computer Science, 1986, pp. 174–187.
O. Goldreich, S. Micali, and A. Wigderson, How to Play Any Mental Game, Proceedings of the 19th Annual ACM Symposium on Theory of Computing, New York, 1987, pp. 218–229.
J. Halpern and M. O. Rabin, A Logic to Reason about Likelihood, Proceedings of the 15th Annual Symposium on the Theory of Computing, 1983, pp. 310–319.
R. Impagliazzo and M. Yung, Direct Minimum Knowledge Computations, in “Advances in Cryptology — CRYPTO 87”, vol. 293 of “Lecture Notes in Computer Science”, Springer Verlag pp. 40–51.
J. Kilian, Founding Cryptography on Oblivious Transfer, Proceedings 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, 1988, pp. 20–31.
J. Kilian, S. Micali, and R. Ostrowsky, Minimum-Resource Zero-Knowledge Proofs, Proceedings of the 30th IEEE Symposium on Foundation of Computer Science, 1989.
R. Ostrowsky and M. Yung, On Necessary Conditions for Secure Distributed Computation, preprint 1989.
T. Rabin and M. Ben-Or, Verifiable Secret Sharing and Multiparty Protocols with Honest Majority, Proceedings of the 21st Annual ACM Symposium on Theory of Computing, Seattle, Washington, 1989, pp. 73–85.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Santis, A., Persiano, G. (1991). Public-Randomness in Public-Key Cryptography. In: Damgård, I.B. (eds) Advances in Cryptology — EUROCRYPT ’90. EUROCRYPT 1990. Lecture Notes in Computer Science, vol 473. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46877-3_5
Download citation
DOI: https://doi.org/10.1007/3-540-46877-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53587-4
Online ISBN: 978-3-540-46877-6
eBook Packages: Springer Book Archive