Algorithms in Group Theory

Postgraduate Thesis uoadl:2216203 316 Read counter

Unit:
Κατεύθυνση Λογική και Θεωρία Αλγορίθμων και Υπολογισμού
Library of the School of Science
Deposit date:
2017-11-15
Year:
2017
Author:
Pilichos Christos
Supervisors info:
Ευάγγελος Ράπτης, Καθηγητής, τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Ελευθέριος Κυρούσης, Καθηγητής, τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Αριστείδης Παγουρτζής, Αναπληρωτής Καθηγητής, τμήμα Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών, Εθνικό Μετσόβειο Πολυτεχνείο
Original Title:
Αλγόριθμοι στη Θεωρία Ομάδων
Languages:
Greek
Translated title:
Algorithms in Group Theory
Summary:
A modern branch of Mathematics is Non-Commutative Cryptography, which is based on the algorithmic hardness of solving some Group Theory based problems. Since 1911, Max Dehn announced that a part of his interest were the word, conjugacy and group-isomorphism problems. The former two accompanied with the analysis problem consist the fundamental problems on which all the protocols of the current Thesis are based on. The tour in the world of Non-Commutative Cryptography begins from the protocols of Wagner-Magyarik (using free groups) and Garzon-Zalcstein (using Grigorchyk's groups) and via Anshel-Anshel-Goldfeld and Ko-Lee et al. (both using braid groups) is over at protocols of Shpilrain-Ushakov (using Thompson's group F), Stickel anf Kurt. Cryptanalysis and the tries of making the above cryptosystems more secure creates some interesting byproducts (like a protocol based on circuits, dynamic version of Stickel's protoocol, using monoids in Wagner-Magyarik protocol, the generalised version of Anshel-Anshel-Goldfeld and Ko-Lee et al. protocols, etc).
Main subject category:
Science
Keywords:
algorithms, cryptography, group theory, non-commutative
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
75
Number of pages:
152
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