Diffie-Hellman-Project

Diffie-Hellman shared-secret derivation in Python, computing the agreed key from public values with hand-written modular exponentiation.

What this demonstrates

Diffie-Hellman lets two parties agree on a shared secret over a public channel without ever sending the secret itself. This works the derivation end to end: given the prime p, generator g, one party's private exponent a, and the other party's public value g^b mod p, it computes the shared key (g^b)^a mod p. The prime is a 512-bit value, so the exponentiation runs on Python big integers.

Concepts demonstrated

• The Diffie-Hellman key exchange: public p and g, private exponents, shared secret g^(ab) mod p
• Modular exponentiation by square-and-multiply (modPower) as the operation that keeps the private exponent hidden
• Deriving the shared secret from one side's private exponent and the other side's public value
• Miller-Rabin primality testing and prime generation (getRandomPrime.py) for producing the group prime

What's implemented

• main.py computes the shared key (g^b)^a mod p from the project's constants. The prime-generation loop is kept inline as commented reference.
• getRandomPrime.py generates probable primes: a trial-division sieve against small primes followed by a Miller-Rabin test (MRTest) with 20 witnesses.

Stack

• Python 3 (standard library, arbitrary-precision integers)

Usage

python main.py

Prints the derived shared secret. The public parameters and private exponent are the values assigned for the project; edit the constants in main.py to run different inputs.