STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Communications of the ACM
Probabilistic encryption & how to play mental poker keeping secret all partial information
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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Alice seeks an information-theoretically secure source of private random data. Unfortunately, she lacks a personal source and must use remote sources controlled by other parties. Alice wants to simulate a coin flip of specified bias α, as a function of data she receives from p sources; she seeks privacy from any coalition of r of them. We show: If p/2≤rp, the bias can be any rational number and nothing else; if 0rp/2, the bias can be any algebraic number and nothing else. The proof uses projective varieties, convex geometry, and the probabilistic method. Our results improve on those laid out by Yao, who asserts one direction of the r=1 case in his seminal paper [yao82]. We also provide an application to secure multiparty computation.