  One-way functions are widely used for encrypting the secret in public key
cryptography, although they are regarded as plausibly one-way but have not been
proven so. Here we discuss the public key cryptosystem based on the system of
higher order Diophantine equations. In this system those Diophantine equations
are used as public keys for sender and recipient, and sender can recover the
secret from the Diophantine equation returned from recipient with a trapdoor.
In general the system of Diophantine equations is hard to solve when it is
positive-dimensional and it implies the Diophantine equations in this
cryptosystem works as a possible one-way function. We also discuss some
problems on implementation, which are caused from additional complexity
necessary for constructing Diophantine equations in order to prevent from
attacking by tamperers.
