Key Exchange Algorithms (Diffie-Hellman, ECDHE)

#Creating Secrets Over Public Channels#link

The 'Holy Grail' of network security is the ability for two parties to agree on a shared secret key without ever sending that key across the wire. If they just sent the key, an eavesdropper would have it. Diffie-Hellman (DH) solved this using the mathematical properties of modular exponentiation.

Standard Diffie-Hellman (DH)

DH uses a large prime number ($p$) and a generator ($g$). Both parties agree on these publicly. Each picks a private secret ($a$ and $b$). They exchange $g^a \pmod p$ and $g^b \pmod p$. Through the magic of algebra, both can then compute $(g^a)^b \pmod p$, which equals $(g^b)^a \pmod p$. An eavesdropper seeing the public values cannot easily find $a$ or $b$ due to the Discrete Logarithm Problem.

# Simple DH simulation (not for production!)
import random

p = 23 # Prime
g = 5  # Generator

# Alice
a_priv = random.randint(1, p-1)
a_pub = pow(g, a_priv, p)

# Bob
b_priv = random.randint(1, p-1)
b_pub = pow(g, b_priv, p)

# Shared Secret
alice_secret = pow(b_pub, a_priv, p)
bob_secret = pow(a_pub, b_priv, p)

print(f'Shared Secret: {alice_secret == bob_secret}' )

While the logic above is correct, the prime $p$ in the real world must be thousands of bits long to prevent attackers from using algorithms like the Number Field Sieve to solve the logarithm.

Perfect Forward Secrecy (PFS) and ECDHE

Elliptic Curve Diffie-Hellman Ephemeral (ECDHE) is the modern standard. 'Ephemeral' means a new key pair is generated for every single session. Even if the server's long-term private key is stolen tomorrow, the attacker cannot decrypt yesterday's traffic because the session keys were never stored and were deleted from memory after the session ended.

Implementation in TLS 1.3

TLS 1.3 has completely removed support for static RSA key exchange. It *mandates* a Diffie-Hellman based exchange (typically ECDHE) to ensure that Perfect Forward Secrecy is guaranteed for every connection.

• ▪Prefer Curve25519 for speed and security
• ▪Disable static RSA key exchange
• ▪Ensure high-entropy random number generation
• ▪Use ephemeral keys for all sessions