Conjugacy in Braid Groups and related Problems + Applications in non-commutative cryptography

We consider the conjugacy problem and its friends (simultaneous and subgroup conjugacy, double coset
problem etc.) in braid and Garside groups. We show how these problems naturally emerge in non-commutative public key cryptography and how they are related. At the end we consider left self-distributive (LD)
systems and my new idea of non-associative cryptography and apply there P. Dehornoy's shifted
conjugacy (and its generalizations).