Date of Degree
Algebra | Information Security
Let F be a finitely generated free group and Aut(F) its group of automorphisms.
In this monograph we discuss potential uses of Aut(F) in group-based cryptography.
Our main focus is on using Aut(F) as a platform group for the Anshel-Anshel-Goldfeld protocol, Ko-Lee protocol, and other protocols based on different versions of the conjugacy search problem or decomposition problem, such as Shpilrain-Ushakov protocol.
We attack the Anshel-Anshel-Goldfeld and Ko-Lee protocols by adapting the existing types of the length-based attack to the specifics of Aut(F). We also present our own version of the length-based attack that significantly increases the attack' success rate. After discussing attacks, we discuss the ways to make keys from Aut(F) resistant to the different versions of length-based attacks including our own.
Shostak, Pavel, "Analysis of a Group of Automorphisms of a Free Group as a Platform for Conjugacy-Based Group Cryptography" (2019). CUNY Academic Works.