Abstract
The study of minimal cryptographic primitives needed to implement secure computation among two or more players is a fundamental question in cryptography. The issue of complete primitives for the case of two players has been thoroughly studied. However, in the multi-party setting, when there are n > 2 players and t of them are corrupted, the question of what are the simplest complete primitives remained open for t ≥ n/3. We consider this question, and introduce complete primitives of minimal cardinality for secure multi-party computation. The cardinality issue (number of players accessing the primitive) is essential in settings where the primitives are implemented by some other means, and the simpler the primitive the easier it is to realize it. We show that our primitives are complete and of minimal cardinality possible.
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. Foundations of secure interactive computation. In Advances in Cryptology-CRYPTO’ 91, LNCS, pp. 377–391. Springer-Verlag, 1992.
M. Ben-Or, S. Goldwasser, and A. Wigderson. Completeness theorems for non-cryptographic fault-tolerant distributed computation. In Proc. 20th ACM Symp. on the Theory of Computing, pp. 1–10, 1988.
M. Blaze. Oblivious Key Escrow. In R. Anderson, editor, Proc.First Infohiding, LNCS, pp. 335–343, Cambridge, U.K., 1996. Springer-Verlag.
A. Beimel, T. Malkin, and S. Micali. The all-or-nothing nature of two-party secure computation. In Advances in Cryptology-CRYPTO’ 99, volume 1666 of LNCS, pp. 80–97. Springer-Verlag, 1999.
R. Canetti. Security and composition of multiparty cryptographic protocols. Journal of Cryptology, 13(1):143–202, 2000.
D. Chaum, C. Crépeau, and I. Damgård. Multiparty unconditionally secure protocols (extended abstract). In Proc. 20th ACM Symp. on the Theory of Computing, pp. 11–19, 1988.
R. Cramer, I. Damgård, S. Dziembowski, M. Hirt, and T. Rabin. Efficient multiparty computations secure against an adaptive adversary. In Advances in Cryptology — EUROCRYPT’ 99, LNCS, 1999.
D. Chaum. The Dining Cryptographers Problem: Unconditional sender and recipient untraceability. Journal of Cryptology, 1(1):65–75, 1988.
V. Chvátal. The tail of the hypergeometric distribution. Discrete Mathematics, 25:285–287, 1979.
D. Dolev, C. Dwork, O. Waarts, and M. Yung. Perfectly secure message transmission. Journal of the ACM, 40(1):17–47, Jan. 1993.
M. J. Fischer, N. A. Lynch, and M. Merritt. Easy impossibility proofs for distributed consensus problems. Distributed Computing, 1:26–39, 1986.
M. Fitzi and U. Maurer. From partial consistency to global broadcast. In 32nd Annual Symp. on the Theory of Computing, pp. 494–503, 2000.
S. Goldwasser and L. Levin. Fair computation of general functions in presence of immoral majority. In Advances in Cryptology — CRYPTO’ 90, volume 537 of LNCS. Springer-Verlag, 1990. g
O. Goldreich, S. Micali, and A. Wigderson. How to play any mental game. In Proc. 19th A CM Symp. on the Theory of Computing, pp. 218–229, 1987.
O. Goldreich. Secure multi-party computation, working draft, version 1.2, Mar. 2000.
J. Kilian. Founding cryptography on oblivious transfer. In Proc. 20th Annual ACM Symp. on the Theory of Computing, pp. 20–31, 2–4 May 1988.
J. Kilian. A general completeness theorem for two-party games. In Proc.23rd Annual ACM Symposium on the Theory of Computing, pp. 553–560, New Orleans, Louisiana, 6–8 May 1991.
J. Kilian. More general completeness theorems for secure two-party computation. In Proc.32nd Annual ACM Symp. on the Theory of Computing, pp. 316–324, Portland, Oregon, 21–23 May 2000.
J. Kilian, E. Kushilevitz, S. Micali, and R. Ostrovsky. Reducibility and completeness in private computations. SIAM Journal on Computing, 29, 1999.
E. Kushilevitz, S. Micali, and R. Ostrovsky. Reducibility and completeness in multi-party private computations. In Proc. 35th Annual IEEE Symp. on the Foundations of Computer Science, pp. 478–491, Nov. 1994.
S. Micali and P. Rogaway. Secure computation. In Advances in Cryptology — CRYPTO’ 91, volume 576 of LNCS, pp. 392–404. Springer-Verlag, 1992.
M. Pease, R. Shostak, and L. Lamport. Reaching agreement in the presence of faults. Journal of the ACM, 27(2):228–234, Apr. 1980.
M. O. Rabin. How to exchange secrets by oblivious transfer. Technical Report TR-81, Harvard Aiken Computation Laboratory, 1981. g
T. Rabin and M. Ben-Or. Verifiable secret sharing and multiparty protocols with honest majority. In Proc. 21st ACM Symp. on the Theory of Computing, pp. 73–85, 1989.
L. G. Valiant. Universal circuits. In ACM Symposium on Theory of Computing (STOC’ 76), pp. 196–203, New York, May 1976. ACM Press.
A. C. Yao. Protocols for secure computations. In Proc. 23rd IEEE Symp. on the Foundations of Computer Science, pp. 160–164. IEEE, 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fitzi, M., Garay, J.A., Maurer, U., Ostrovsky, R. (2001). Minimal Complete Primitives for Secure Multi-party Computation. In: Kilian, J. (eds) Advances in Cryptology — CRYPTO 2001. CRYPTO 2001. Lecture Notes in Computer Science, vol 2139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44647-8_5
Download citation
DOI: https://doi.org/10.1007/3-540-44647-8_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42456-7
Online ISBN: 978-3-540-44647-7
eBook Packages: Springer Book Archive