  The braid group is an important non commutative group, at the same time, it
is an important tool in quantum field theory with better topological structure,
and often used as a research carrier for anti-quantum cryptographic algorithms.
This paper proposed a difficult problem on a positive braid semi-group, and
proved that the difficulty is not lower than the conjugate search problem.
Based on this new difficult problem, we propose a new cryptosystem, which
include a key exchange protocol and a public key encryption algorithm. Since
our cryptosystem is implemented on a semi-group, it effectively avoids the
analysis of attack algorithms on the cluster and makes our algorithm more
secure.
