STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Robust sharing of secrets when the dealer is honest or cheating
Journal of the ACM (JACM)
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Efficient Multiparty Protocols Using Circuit Randomization
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Round-Efficient Secure Computation in Point-to-Point Networks
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
An Unconditionally Secure Protocol for Multi-Party Set Intersection
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Round Efficient Unconditionally Secure Multiparty Computation Protocol
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Information Theoretically Secure Multi Party Set Intersection Re-visited
Selected Areas in Cryptography
Efficient multiparty computations secure against an adaptive adversary
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Simple and efficient perfectly-secure asynchronous MPC
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Perfectly-secure MPC with linear communication complexity
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Privacy-preserving set operations
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Efficient multi-party computation with dispute control
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Fair and privacy-preserving multi-party protocols for reconciling ordered input sets
ISC'10 Proceedings of the 13th international conference on Information security
Secure efficient multiparty computing of multivariate polynomials and applications
ACNS'11 Proceedings of the 9th international conference on Applied cryptography and network security
On the power of correlated randomness in secure computation
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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In information theoretic model, unconditionally secure multiparty computation (UMPC) allows a set of n parties to securely compute an agreed function f, even upto t n/2 parties are under the control of an active adversary having unbounded computing power. The bound on the resilience/fault tolerance (i.e t n/2 ) is optimal, as long as each party is connected with every other party by a secure channel and a common physical broadcast channel is available to the parties and a negligible error probability of $2^{-{\it \Omega}(\kappa)}$ (for some security parameter 驴) is allowed in the computation. Any UMPC protocol designed under the above settings is called as optimally resilient UMPC protocol. In this paper, we propose an optimally resilient UMPC protocol with n = 2t + 1, which requires only ${\cal O}({\cal D})$ rounds, where ${\cal D}$ is the multiplicative depth of the arithmetic circuit representing f. To the best of our knowledge, our protocol is the first UMPC protocol with optimal resilience, to attain a round complexity that is independent of n. When ${\cal D}$ is constant, then our protocol requires only constant number of rounds. Our protocol is to be compared with the most round efficient, optimally resilient, UMPC protocol of [16] that requires ${\cal O}(\log{n} + {\cal D})$ rounds in the same settings as ours. Thus our UMPC significantly reduces the round complexity of [16]. Moreover, our UMPC protocol requires the same communication complexity as that of [16]. As a tool for designing our UMPC protocol, we propose a new and robust multiplication protocol to generate t-sharing of the product of two t-shared secrets.As an interesting, practically-on-demand MPC problem, we present a protocol for unconditionally secure multiparty set intersection (UMPSI) with optimal resilience; i.e., with n = 2t + 1, having a negligible error probability in correctness. This protocol adapts the techniques used in our proposed general UMPC protocol. The protocol takes constant number rounds, incurs a private communication of ${\cal O}(m^2n^4 \kappa)$ bits and broadcasts ${\cal O}((m^2n^4 + n^5)\kappa)$ bits, where each party has a set of size m. To the best of our knowledge, this is the first ever UMPSI protocol with n = 2t + 1. This solves an open problem posed in [15] and [17], urging to design an UMPSI protocol with n = 2t + 1. Our UMPSI protocol is to be compared with the best known UMPSI protocol of [17] with n = 3t + 1 (i.e., non-optimal resilience), which takes constant number rounds, incurs a private communication of ${\cal O}((m^2n^3 + n^4 \kappa)\kappa)$ bits and broadcasts ${\cal O}((m^2n^3 + n^4 \kappa)\kappa)$ bits. So even though the communication complexity of our UMPSI protocol is slightly larger than that of [17], our UMPSI protocol significantly improves the resilience of UMPSI protocol of [17]; i.e., from t n / 3 to t n / 2.