## IACR paper details

Title | Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups |
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Booktitle | IACR Eprint archive |
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Pages | |
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Year | 2002 |
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URL | http://eprint.iacr.org/2002/036 |
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Author | Ronald Cramer |
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Author | Serge Fehr |
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Abstract |
A {\em black-box} secret sharing scheme for the threshold
access structure $T_{t,n}$ is one which works over any finite Abelian group $G$.
Briefly, such a scheme differs from an ordinary linear secret sharing
scheme (over, say, a given finite field) in that distribution matrix
and reconstruction vectors are defined over the integers and are designed {\em
independently} of the group $G$ from which the secret and the shares
are sampled. This means that perfect completeness and perfect
privacy are guaranteed {\em regardless} of which group $G$ is chosen. We define
the black-box secret sharing problem as the problem of devising, for
an arbitrary given $T_{t,n}$, a scheme with minimal expansion factor,
i.e., where the length of the full vector of shares divided by the
number of players $n$ is minimal.
Such schemes are relevant for instance in the context of distributed
cryptosystems based on groups with secret or hard to compute group
order. A recent example is secure general multi-party computation over
black-box rings.
In 1994 Desmedt and Frankel have proposed an
elegant approach to the black-box secret sharing problem
based in part on polynomial interpolation over
cyclotomic number fields. For arbitrary given $T_{t,n}$ with
$0 |
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Search for the paper

@misc{eprint-2002-11560,
title={Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups},
booktitle={IACR Eprint archive},
keywords={cryptographic protocols / information theoretically secure secret sharing,},
url={http://eprint.iacr.org/2002/036},
note={ cramer@daimi.aau.dk 11767 received 21 Mar 2002, last revised 21 Mar 2002},
author={Ronald Cramer and Serge Fehr},
year=2002
}

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