TY - JOUR
T1 - Analysis of secret sharing schemes based on Nielsen transformations
AU - Kotov, Matvei
AU - Panteleev, Dmitry
AU - Ushakov, Alexander
N1 - Publisher Copyright:
© 2018 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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.
AB - 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.
KW - Cryptography
KW - Nielsen transformations
KW - group-based cryptography
KW - secret sharing
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U2 - 10.1515/gcc-2018-0001
DO - 10.1515/gcc-2018-0001
M3 - Article
AN - SCOPUS:85046006286
SN - 1867-1144
VL - 10
SP - 1
EP - 8
JO - Groups, Complexity, Cryptology
JF - Groups, Complexity, Cryptology
IS - 1
ER -