Travelling salesman cryptosystem

We propose a public key cryptosystem using the traveling salesman problem that is a NP-complete problem. First, we show the outline on the traveling salesman cryptosystem, then investigate sequences used as the secret key in the traveling salesman cryptosystem. Next, we consider the public key generation for the traveling salesman cryptosystem, further propose the new encryption using the mixed sum and product operations. Finally, we examine the security of this cryptosystem against the attack using Shamir algorithm and LLL algorithm.