Moldenhauer, Anja I. S.
[Verfasser:in]
;
Rosenberger, Gerhard
[Mitwirkende:r]
Cryptographic protocols based on inner product spaces and group theory with a special focus on the use of Nielsen transformations ; Kryptographische Protokolle basierend auf Vektorräumen mit innerem Produkt und Gruppentheorie mit einem speziellen Fokus auf Nielsen-Transformationen
Titel:
Cryptographic protocols based on inner product spaces and group theory with a special focus on the use of Nielsen transformations ; Kryptographische Protokolle basierend auf Vektorräumen mit innerem Produkt und Gruppentheorie mit einem speziellen Fokus auf Nielsen-Transformationen
Beteiligte:
Moldenhauer, Anja I. S.
[Verfasser:in]
Erschienen:
Staats- und Universitätsbibliothek Hamburg Carl von Ossietzky, 2016-01-01
Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
The topic of this thesis is established in the area of mathematical cryptology, more precisely in group based cryptology. We give extensions of cryptographic protocols, develop new cryptographic protocols concerning the mathematical background and give modifications of them. In addition cryptographic analysis as well as examples are given. The focus lays on the development of new cryptographic protocols using non-commutative groups and of techniques, which are typically studied in combinatorial group theory. Automorphisms on finitely generated free groups are used, which can be generated by Nielsen transformations or Whitehead-Automorphisms. With the help of the Whitehead-Automorphisms we develop an approach for choosing automorphisms randomly of the automorphism group Aut(F), with F a finitely generated free group. Altogether twelve cryptographic protocols are explained. Among these are two extensions of a (n,t)-secret sharing protocol, which is introduced by C. S. Chum, B. Fine, G. Rosenberger and X. Zhang. Both extensions depend on the Closest Vector Theorem in a real inner product space. The first one (Protocol 1) is a symmetric key cryptosystem and the second one is a challenge and response system (Protocol 2), which can be used by a variation as a two-way authentication. Furthermore, the HKKS-key exchange protocol by M. Habbeb, D. Kahrobaei, C. Koupparis and V. Shpilrain, which uses semidirect products of (semi)groups, is extended to an ElGamal like public key cryptosystem (Protocol 3) and to a signature protocol (Protocol 4). There is an ongoing research about the HKKS-key exchange protocol with linear algebra attacks as well as research about suitable platforms, which also affects the ElGamal like public key cryptosystem and the signature protocol. A short overview of the research is given in this thesis. Furthermore, a purely combinatorial secret sharing scheme (Protocol 5) is introduced, which uses a share distribution method explained by D. Panagopoulos for a (n,t)-secret sharing scheme. We show that ...