On perfectly secure communication over arbitrary networks
Proceedings of the twenty-first annual symposium on Principles of distributed computing
Non-perfect Secret Sharing over General Access Structures
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Asynchronous Secure Communication Tolerating Mixed Adversaries
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Corruption and Recovery-Efficient Locally Decodable Codes
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Alternative protocols for generalized oblivious transfer
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
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Abstract: A secret-sharing scheme enables a dealer to distribute a secret among n parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f : {0, 1}^n\rightarrow {0, 1}. A family of secret-sharing schemes is called efficient if the total length of the n shares is polynomial in n. Most previously known secret-sharing schemes belonged to a class of linear schemes, whose complexity coincides with the monotone span program size of their access structure. Prior to this work there was no evidence that nonlinear schemes can be significantly more efficient than linear schemes, and in particular there were no candidates for schemes efficiently realizing access structures which do not lie in NC. The main contribution of this work is the construction of two efficient nonlinear schemes: (1) A scheme with perfect privacy whose access structure is conjectured not to lie in NC; (2) A scheme with statistical privacy whose access structure is conjectured not to lie in P/poly. Another contribution is the study of a class of nonlinear schemes, termed quasi-linear schemes, obtained by composing linear schemes over different fields. We show that while these schemes are possibly (super-polynomially) more powerful than linear schemes, they cannot efficiently realize access structures outside NC.