The dining cryptographers problem: unconditional sender and recipient untraceability
Journal of Cryptology
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
Unconditional sender and recipient untraceability in spite of active attacks
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Elements of information theory
Elements of information theory
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
A communication-privacy tradeoff for modular addition
Information Processing Letters
A minimal model for secure computation (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Secure hypergraphs: privacy from partial broadcast
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Randomness complexity of private computation
Computational Complexity
Private Simultaneous Messages Protocols with Applications
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
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In this paper we introduce a new model for private computation, the Shared Randomness over Broadcast Channel model (SRoBC for short). Following the classical model for private computation [2,4], we consider a set of n computationally unbounded honest but curious players P1, . . . , Pn with private inputs x1, x2, . . . ,xn. The players wish to compute a function f of their inputs in a private way. Unlike in the classical model, no private channel is available to the players but all the communication takes place using a broadcast channel. Moreover, the only available source of randomness is a shared random string.We show that even in this minimal setting private computation is possible: we present a protocol for computing the sum modulo 2 in a t-private way in the SRoBC model. The protocol uses n(t+1)/2 random bits. We show that this is the optimal randomness complexity in the case each random bit is shared between two players (low-contention protocols). We further show that, in the case t = 1, this protocol is optimal with respect to the randomness complexity regardless of the contention of the protocol.