Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Analysis of secret sharing schemes based on Nielsen transformations

Analysis of secret sharing schemes based on Nielsen transformations AbstractWe investigate security properties of two secret-sharing protocolsproposed by Fine, Moldenhauer, and Rosenbergerin 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 equationsand (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{m-1}shares reduces the space of possible valuesof a secret to a set of polynomial size. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Analysis of secret sharing schemes based on Nielsen transformations

Loading next page...
 
/lp/de-gruyter/analysis-of-secret-sharing-schemes-based-on-nielsen-transformations-L23HPmUCHD
Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2018-0001
Publisher site
See Article on Publisher Site

Abstract

AbstractWe investigate security properties of two secret-sharing protocolsproposed by Fine, Moldenhauer, and Rosenbergerin 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 equationsand (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{m-1}shares reduces the space of possible valuesof a secret to a set of polynomial size.

Journal

Groups Complexity Cryptologyde Gruyter

Published: May 1, 2018

References