### Error Decodable Secret Sharing and One-Round Perfectly Secure Message Transmission for General Adversary Structures

Keith M. Martin, Maura B. Paterson, and Douglas R. Stinson

##### Abstract

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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Keywords
secret sharingperfectly secure message transmissionerror correction
Contact author(s)
m paterson @ bbk ac uk
History
Short URL
https://ia.cr/2009/487

CC BY

BibTeX

@misc{cryptoeprint:2009/487,
author = {Keith M.  Martin and Maura B.  Paterson and Douglas R.  Stinson},
title = {Error Decodable Secret Sharing and One-Round Perfectly Secure Message Transmission for General Adversary Structures},
howpublished = {Cryptology ePrint Archive, Paper 2009/487},
year = {2009},
note = {\url{https://eprint.iacr.org/2009/487}},
url = {https://eprint.iacr.org/2009/487}
}

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