Analysis of secret sharing schemes based on Nielsen transformations
Author:
Kotov Matvei,Panteleev Dmitry,Ushakov Alexander
Abstract
Abstract
We investigate security properties of two secret-sharing protocols
proposed by Fine, Moldenhauer, and Rosenberger
in Sections 4 and 5 of [B. Fine, A. Moldenhauer and G. Rosenberger,
Cryptographic protocols based on Nielsen transformations,
J. Comput. Comm. 4 2016, 63–107]
(Protocols I and II resp.).
For both protocols, we consider a one missing share challenge.
We show that Protocol I can be reduced to a system of polynomial equations
and (for most randomly generated instances)
solved by the computer algebra system Singular.
Protocol II is approached using the technique of Stallings’ graphs.
We show that knowledge of
{m-1}
shares reduces the space of possible values
of a secret to a set of polynomial size.
Funder
National Science Foundation
Publisher
Walter de Gruyter GmbH
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Computer Networks and Communications
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