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@inproceedings{Cheraghchi:2016:10.1109/ISIT.2016.7541751,
author = {Cheraghchi, Bashi Astaneh M},
doi = {10.1109/ISIT.2016.7541751},
pages = {2509--2513},
publisher = {IEEE},
title = {Nearly optimal robust secret sharing},
url = {http://dx.doi.org/10.1109/ISIT.2016.7541751},
year = {2016}
}

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TY  - CPAPER
AB  - Abstract:We prove that a known approach to improve Shamir's celebrated secret sharing scheme; i.e., adding an information-theoretic authentication tag to the secret, can make it robust for n parties against any collusion of size δn, for any constant δ ∈ (0; 1/2). This result holds in the so-called “nonrushing” model in which the n shares are submitted simultaneously for reconstruction. We thus finally obtain a simple, fully explicit, and robust secret sharing scheme in this model that is essentially optimal in all parameters including the share size which is k(1+o(1))+O(κ), where k is the secret length and κ is the security parameter. Like Shamir's scheme, in this modified scheme any set of more than δn honest parties can efficiently recover the secret. Using algebraic geometry codes instead of Reed-Solomon codes, the share length can be decreased to a constant (only depending on δ) while the number of shares n can grow independently. In this case, when n is large enough, the scheme satisfies the “threshold” requirement in an approximate sense; i.e., any set of δn(1 + ρ) honest parties, for arbitrarily small ρ > 0, can efficiently reconstruct the secret.
AU  - Cheraghchi,Bashi Astaneh M
DO  - 10.1109/ISIT.2016.7541751
EP  - 2513
PB  - IEEE
PY  - 2016///
SN  - 2157-8117
SP  - 2509
TI  - Nearly optimal robust secret sharing
UR  - http://dx.doi.org/10.1109/ISIT.2016.7541751
UR  - http://hdl.handle.net/10044/1/30874
ER  -

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Dr Mahdi Cheraghchi

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