Abstract
This paper addresses the message complexity of secure computation in the (passive adversary) privacy setting. We show that O(nC) encrypted bits of communication suffice for n parties to evaluate any boolean circuit of size C privately, under a specific cryptographic assumption. This work establishes a connection between secure distributed computation and group-oriented cryptography, i.e., cryptographic methods in which subsets of individuals can act jointly as single agents. Our secure computation protocol relies on a new group-oriented probablistic public-key encryption scheme with useful algebraic properties.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Chaum, I. Damgård, and J. van de Graaf, Multiparty computations ensuring privacy of each party's input and correctness of the result, Advances in Cryptology—CRYPTO '87 Proceedings (Lecture Notes in Computer Science, Vol. 293), ed. C. Pomerance, pp. 87–119, Springer-Verlag, Berlin, 1988.
Y. Desmedt, Society and group oriented cryptography: a new concept, Advances in Cryptology—CRYPTO '87 Proceedings (Lecture Notes in Computer Science, Vol. 293), ed. C. Pomerance, pp. 120–127, Springer-Verlag, Berlin, 1988.
Y. Desmedt and Y. Frankel, Threshold cryptosystems, Advances in Cryptology—CRYPTO '89 Proceedings (Lecture Notes in Computer Science, Vol. 435), ed. G. Brassard, pp. 307–315, Springer-Verlag, Berlin, 1990.
W. Diffie and M. Hellman, New directions in cryptography, IEEE Transactions on Information Theory, 22(6):644–654, 1976.
T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Transactions on Information Theory, 31:469–472, 1985.
Z. Galil, S. Haber, and M. Yung, Cryptographic computation: secure fault-tolerant protocols and the public-key model, Advances in Cryptography—CRYPTO '87 Proceedings (Lecture Notes in Computer Science, Vol. 293), ed. C. Pomerance, pp. 135–155, Springer-Verlag, Berlin, 1988.
O. Goldreich, S. Micali, and A. Wigderson, How to play any mental game, Proceedings of the 19th Annual Symposium on Theory of Computing, 1987, pp. 218–229.
O. Goldreich and R. Vainish, How to solve any protocol problem—an efficiency improvement, Advances in Cryptology—CRYPTO '87 Proceedings (Lecture Notes in Computer Science, Vol. 293), ed. C. Pomerance, pp. 73–86, Springer-Verlag, Berlin, 1988.
S. Goldwasser and S. Micali, Probabilistic encryption, Journal of Computer and System Sciences, 28:270–299, 1984.
K. McCurley, A key distribution system equivalent to factoring, Journal of Cryptology, 1:95–105, 1988.
S. Micali, Fair public-key cryptosystems, Advances in Cryptology—CRYPTO '92 Proceedings (Lecture Notes in Computer Science, Vol. 740), ed. E. Brickell, pp. 114–139, Springer-Verlag, Berlin, 1993.
Z. Shmuely, Composite Diffie-Hellman public-key generating systems are hard to break, Technical Report #356, Technion—Israel Institute of Technology, February 1985.
A. Yao, Protocols for secure computations, Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, 1982, pp. 160–164.
A. Yao, How to generate and exchange secrets, Proceedings of the 27th Annual Symposium on Foundations of Computer Science, 1986, pp. 162–167.
Author information
Authors and Affiliations
Additional information
Communicated by Joan Feigenbaum
Work performed while at Columbia University, with the support of a summer internship at Bellcore and a visiting position at C.W.I.
Rights and permissions
About this article
Cite this article
Franklin, M., Haber, S. Joint encryption and message-efficient secure computation. J. Cryptology 9, 217–232 (1996). https://doi.org/10.1007/BF00189261
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00189261