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Universally Ideal Secret Sharing Schemes
 IEEE Trans. on Information Theory
, 1994
"... Given a set of parties f1; : : : ; ng, an access structure is a monotone collection of subsets of the parties. For a certain domain of secrets, a secret sharing scheme for an access structure is a method for a dealer to distribute shares to the parties. These shares enable subsets in the access stru ..."
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Given a set of parties f1; : : : ; ng, an access structure is a monotone collection of subsets of the parties. For a certain domain of secrets, a secret sharing scheme for an access structure is a method for a dealer to distribute shares to the parties. These shares enable subsets in the access structure to reconstruct the secret, while subsets not in the access structure get no information about the secret. A secret sharing scheme is ideal if the domains of the shares are the same as the domain of the secrets. An access structure is universally ideal if there exists an ideal secret sharing scheme for it over every finite domain of secrets. An obvious necessary condition for an access structure to be universally ideal is to be ideal over the binary and ternary domains of secrets. In this work, we prove that this condition is also sufficient. We also show that being ideal over just one of the two domains does not suffice for universally ideal access structures. Finally, we give an exac...
On the bound for anonymous secret sharing schemes
 Discrete Appl. Math
, 2002
"... In anonymous secret sharing schemes, the secret can be reconstructed without knowledge of which participants hold which shares. In this paper, we derive a tighter lower bound on the size of the shares than the bound of Blundo and Stinson for anonymous (k, n)threshold schemes with 1 < k < n. Ou ..."
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In anonymous secret sharing schemes, the secret can be reconstructed without knowledge of which participants hold which shares. In this paper, we derive a tighter lower bound on the size of the shares than the bound of Blundo and Stinson for anonymous (k, n)threshold schemes with 1 < k < n. Our bound is tight for k = 2. We also show a close relationship between optimum anonymous (2, n)threshold secret schemes and combinatorial designs.
Almostperfect secret sharing
 ISIT'11: INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, RUSSIAN FEDERATION
, 2011
"... To split a secret s between several participants, we generate (for each value of s) shares for all participants. The goal: authorized groups of participants should be able to reconstruct the secret but forbidden ones get no information about it. We introduce several notions of nonperfect secret sha ..."
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To split a secret s between several participants, we generate (for each value of s) shares for all participants. The goal: authorized groups of participants should be able to reconstruct the secret but forbidden ones get no information about it. We introduce several notions of nonperfect secret sharing, where some small information leak is permitted. We study its relation to the Kolmogorov complexity version of secret sharing (establishing some connection in both directions) and the effects of changing the secret size (showing that we can decrease the size of the secret and the information leak at the same time).