Iterated LD-Problem in non-associative key establishment

We construct new non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and mutual LD-systems. The hardness of these protocols relies on variations of the (simultaneous) iterated LD-problem and its generalizations. We discuss instantiations of these protocols using generalized shifted conjugacy in braid groups and their quotients, LD-conjugacy and $f$-symmetric conjugacy in groups. We suggest parameter choices for instantiations in braid groups, symmetric groups and several matrix groups.Comment: 30 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1305.440

Analysis of a Group of Automorphisms of a Free Group as a Platform for Conjugacy-Based Group Cryptography

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\u27 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