Myasnikov (City College of New York) et al. apply the complexity of non-commutative groups
to public key cryptography, assess the generic-case performance of various algorithms, and …

This book is about relations between three di? erent areas of mathematics and
theoreticalcomputer science: combinatorialgroup theory, cryptography, and c-plexity theory …

We introduce the linear centralizer method, and use it to devise a provable polynomial-time
solution of the Commutator Key Exchange Problem, the computational problem on which, in …

The conjugacy search problem in a group G is the problem of recovering an x ∈ G from
given g ∈ G and h= x− 1 gx. This problem is in the core of several recently suggested public …

We offer cryptanalysis of a key exchange scheme due to Stickel [11], which was inspired by
the well-known Diffie-Hellman protocol. We show that Stickel's choice of platform (the group …

This paper introduces a new type of attack, termed a nonlinear decomposition attack,
against two known group-based key agreement protocols, namely, protocol based on …

In this paper we present a new key establishment protocol based on the decomposition
problem in non-commutative groups which is: given two elements $ w, w_1 $ of the platform …

In this paper we present a practical heuristic attack on the Ko, Lee et al. key exchange
protocol introduced at Crypto 2000 [11]. Using this attack, we were able to break the protocol …

In the last decade, a number of public-key cryptosystems based on combinatorial group
theoretic problems in braid groups have been proposed. We survey these cryptosystems …

The goalofthisbookis toshowcasenewdirectionsingroup theorymotivated bycomputer
science. The subtitle (GAGTA book) reflects the fact that the book follows the courseoftheGeometricandAsymptoticGroup …