Abstract
We show that a complete broadcast network of n processors can evaluate any function f x 1,...,x n) at private inputs supplied by each processor, revealing no information other than the result of the function, while tolerating up to t maliciously faulty parties for 2t < n. This improves the previous bound of 3t < n on the tolerable number of faults [BGW88, CCD88]. We demonstrate a resilient method to multiply secretly shared values without using unproven cryptographic assumptions. The crux of our method is a new, non-cryptographic zero-knowledge technique which extends verifiable secret sharing to allow proofs based on secretly shared values. Under this method, a single party can secretly share values v 1,...,v m along with another secret w = P(v 1,...,v m), where P is any polynomial size circuit; and she can prove to all other parties that w = P(v 1,...,v m), without revealing w or any other information. Our protocols allow an exponentially small chance of error, but are provably optimal in their resilience against Byzantine faults. Furthermore, our solutions use operations over exponentially large fields, greatly reducing the amount of interaction necessary for computing natural functions.
This research was supported in part under NSF grant CCR-870-4513.
Chapter PDF
References
D. Beaver, J. Bar-Han. “Non-Cryptographic Fault-Tolerant Computing in a Constant Expected Number of Rounds of Interaction.” Proc. of 21st STOC (1989), 201–209.
D. Beaver. “Secure Multiparty Protocols Tolerating Half Faulty Processors.” Technical Report TR-19-88 (September, 1988), Harvard University.
M. Ben-Or, S. Goldwasser, A. Wigderson. “Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation.” Proc. of 20th STOC (1988), 1–10.
G. R. Blakley, “Security Proofs for Information Protection Systems.” Proceedings of the 1980 Symposium on Security and Privacy, IEEE Computer Society Press, NY (1981), 79–88.
M. Ben-Or, T. Rabin. “Verifiable Secret Sharing and Multiparty Protocols with Honest Majority.” 21st STOC (1989), 73–85.
D. Chaum, C. Crépeau, I. Damgård. “Multiparty Unconditionally Secure Protocols.” Proc. of 20th STOC (1988), 11–19.
B. Chor, S. Goldwasser, S. Micali, B. Awerbuch. “Verifiable Secret Sharing and Achieving Simultaneity in the Presence of Faults.” Proc. of 17th STOC (1985), 383–395.
S. Goldwasser, S. Micali, C. Rackoff. “The Knowledge Complexity of Interactive Proof Systems.” SIAM Journal on Computing 18, no. 1 (1989), 186–208.
Goldreich, O., Micali, S., A. Wigderson. “How to Play Any Mental Game, or A Completeness Theorem for Protocols with Honest Majority.” Proc. of 19th STOC (1987), 218–229.
J. Kilian, personal communication.
J. Kilian. “Founding Cryptography on Oblivious Transfer.” Proc. of 20th STOC (1988), 20–29.
T. Rabin. “Robust Sharing of Secrets When the Dealer is Honest or Cheating.” Masters Thesis, Hebrew University, 1988.
A. Shamir. “How to Share a Secret.” CACM 22 (1979), 612–613.
A. Yao. “How to Generate and Exchange Secrets.” Proc. of 27th FOCS (1986), 162–167.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beaver, D. (1990). Multiparty Protocols Tolerating Half Faulty Processors. In: Brassard, G. (eds) Advances in Cryptology — CRYPTO’ 89 Proceedings. CRYPTO 1989. Lecture Notes in Computer Science, vol 435. Springer, New York, NY. https://doi.org/10.1007/0-387-34805-0_49
Download citation
DOI: https://doi.org/10.1007/0-387-34805-0_49
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97317-3
Online ISBN: 978-0-387-34805-6
eBook Packages: Springer Book Archive