Abstract: A public key cryptographic system and method includes an insecure communications channel connecting at least two communicating complexes, a sender and a receiver. The sender possesses an encoding device and the receiver possesses a decoding device. The sender uses a public key that may be known by an unauthorized receiver and that is generated by random processes known only to the receiver to encrypt a plain text destined for the receiver. The transformation of plain text to encrypted text using the public key is easily performed, but the inversion of that transformation using only the public key information and the knowledge of the operations of encryption and decryption is extremely difficult and computationally infeasible. The receiver uses the knowledge of the randomly generated transformation set components (the private key) to easily and incrementally invert the encrypted text and recover the plain text.