An Alternative Diffie-Hellman Method … and What is (mod 1)?
In 1978, Whitfield Diffie and Martin Hellman created the Diffie-Hellman key exchange method, and which has since become one of the foundation principles of cybersecurity. With this, Bob and Alice agree on a generator value (g) and a prime number (p). To generate a shared key, Alice generates a random value (a) and computes A=g^a (mod p), and sends A to Bob. Bob generates a random value (b) and computes B=g^b (mod p), and send B to Alice. Alice then calculates the shared value of B^a (mod p) and Bob calculates the shared value of A^b (mod p). This value will be g^{ab} (mod p), and where (mod p) is the remainder of an integer divide by p.
These days we tend not to use discrete log methods, and use elliptic curve methods, instead. With this A=aG, and B=bG, and where the shared secrets will be K_1=bA and K_2=aB. This method is known as Elliptic Curve Diffie-Hellman (ECDH) and where G is the base point on the curve.
In 2020, E Järpe outlined an alternative Diffie-Hellman method [1]. It uses the (mod1) operation and relies on the values calculated from the fractional part of a multiplication:
