5 research outputs found
Error Decodable Secret Sharing and One-Round Perfectly Secure Message Transmission for General Adversary Structures
An error decodable secret-sharing scheme is a secret-sharing
scheme with the additional property that the secret can be
recovered from the set of all shares, even after a coalition of
participants corrupts the shares they possess. In this paper we
consider schemes that can tolerate corruption by sets of
participants belonging to a monotone coalition structure, thus
generalising both a related notion studied by Kurosawa, and the
well-known error-correction properties of threshold schemes based
on Reed-Solomon codes. We deduce a necessary and sufficient
condition for the existence of such schemes, and we show how to
reduce the storage requirements of a technique of Kurosawa for
constructing error-decodable secret-sharing schemes with efficient
decoding algorithms.
In addition, we explore the connection between one-round perfectly
secure message transmission (PSMT) schemes with general adversary
structures and secret-sharing schemes, and we exploit this
connection to investigate factors affecting the performance of
one-round PSMT schemes such as the number of channels required,
the communication overhead, and the efficiency of message recovery
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes
We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance
Error decodable secret sharing and one-round perfectly secure message transmission for general adversary structures
An error decodable secret-sharing scheme is a secret-sharing scheme with the additional property that the secret can be recovered from the set of all shares, even after a coalition of participants corrupts the shares they possess. In this paper, schemes that can tolerate corruption by sets of participants belonging to a monotone coalition structure are considered. This coalition structure may be unrelated to the authorised sets of the secret-sharing scheme. This is generalisation of both a related notion studied in the context of multiparty computation, and the well-known error-correction properties of threshold schemes based on Reed-Solomon codes. Necessary and sufficient conditions for the existence of such schemes are deduced, and methods for reducing the storage requirements of a technique of Kurosawa for constructing error-decodable secret-sharing schemes with efficient decoding algorithms are demonstrated. In addition, the connection between one-round perfectly secure message transmission (PSMT) schemes with general adversary structures and secret-sharing schemes is explored. We prove a theorem that explicitly shows the relation between these structures. In particular, an error decodable secret-sharing scheme yields a one-round PSMT, but the converse does not hold. Furthermore, we are able to show that some well-known results concerning one-round PSMT follow from known results on secret-sharing schemes. These connections are exploited to investigate factors affecting the performance of one-round PSMT schemes such as the number of channels required, the communication overhead, and the efficiency of message recovery