Cryptographic method and system for secure authentication and key exchange

A computer-implemented method of authentication between parties, comprising:

• a) receiving a randomly generated binary string, having a pre-agreed integer value;
• b) combining a shared secret of the parties with the randomly generated binary string to form a new binary string;
• c) initiating a binary pair (A, B) with an initial value of (A0, B0);
• d) reading a first bit of the new binary string;
• e) adding a current value of B to A when the read bit is zero;
• f) adding a current value of A to B when the read bit is one;
• g) reading a next bit of the new binary string;
• repeating steps e through g in a loop process, via a processor, until all bits of the new binary string have been read;
• returning a final binary pair (A, B) after all of the bits have been read;
• securely exchanging ephemeral Diffie-Hellman (DH) public keys between the parties;
• and
• exchanging challenge responses and agreeing on a session key between the parties.