Analysis of secret sharing schemes based on Nielsen transformations

Matvei Kotov, Dmitry Panteleev, Alexander Ushakov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalGroups, Complexity, Cryptology
Volume10
Issue number1
DOIs
StatePublished - 1 May 2018

Keywords

  • Cryptography
  • Nielsen transformations
  • group-based cryptography
  • secret sharing

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