Abstract
We revisit the following open problem in information-theoretic cryptography: Does the communication complexity of unconditionally secure computation depend on the computational complexity of the function being computed? For instance, can computationally unbounded players compute an arbitrary function of their inputs with polynomial communication complexity and a linear threshold of unconditional privacy? Can this be done using a constant number of communication rounds?
We provide an explanation for the difficulty of resolving these questions by showing that they are closely related to the problem of obtaining efficient protocols for (information-theoretic) private information retrieval and hence also to the problem of constructing short locally-decodable error-correcting codes. The latter is currently considered to be among the most intriguing open problems in complexity theory.
Research supported in part by a grant from the Israel Science Foundation and by the Technion V.P.R. Fund.
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Ishai, Y., Kushilevitz, E. (2004). On the Hardness of Information-Theoretic Multiparty Computation. In: Cachin, C., Camenisch, J.L. (eds) Advances in Cryptology - EUROCRYPT 2004. EUROCRYPT 2004. Lecture Notes in Computer Science, vol 3027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24676-3_26
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