Abstract: A method and algorithm of authentication between parties includes receiving a randomly generated binary string. A shared secret of the parties is combined with the randomly generated binary string to form a new binary string. A binary pair (A, B) is initiated; a first bit of the new binary string is read. A current value of B is added to A when the read bit is zero, and a current value of A is added to B when the read bit is one. A next bit of the new binary string is read. The steps of adding the current values and reading a next bit are repeated until all bits have been read. A resulting binary pair (A, B) is returned after all of the bits have been read. Ephemeral Diffie-Hellman public keys are securely exchanged between the parties. Challenge responses are exchanged and a session key is agreed upon.

Abstract: A method and algorithm of authentication between parties includes receiving a randomly generated binary string. A shared secret of the parties is combined with the randomly generated binary string to form a new binary string. A binary pair (A, B) is initiated; a first bit of the new binary string is read. A current value of B is added to A when the read bit is zero, and a current value of A is added to B when the read bit is one. A next bit of the new binary string is read. The steps of adding the current values and reading a next bit are repeated until all bits have been read. A resulting binary pair (A, B) is returned after all of the bits have been read. Ephemeral Diffie-Hellman public keys are securely exchanged between the parties. Challenge responses are exchanged and a session key is agreed upon.