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.