  Traditional methods in public key cryptography are based on number theory,
and suffer from problems such as dealing with very large numbers, making key
creation cumbersome. Here, we propose a new public key cryptosystem based on
strings only, which avoids the difficulties of the traditional number theory
approach. The security mechanism for public and secret keys generation is
ensured by a recursive encoding mechanism embedded in a
quasi-commutative-random function, resulted from the composition of a
quasi-commutative function with a pseudo-random function. In this revised
version of the paper we show that the eavesdropper's problem of the proposed
cryptosystem has a solution, and we give the details of the solution.
