1. Public Key Cryptography
Diffie – Hellman
(Key Exchange Algorithm)
Dr. Chandresh Parekh
School of IT, AI & Cyber Security
Rashtriya Raksha University
2. Concept
• Sender and Receiver derive a shared secret key over a
public channel (no prior arrangements)
• Publicly agree on two public values, and
• Each choose a private value, and
• Use clever math to compute a shared secret key,
• Attackers never overhear enough information to derive the
shared secret key
3. Math : Discrete Logarithm Problem
Let be a large prime number
Let be an integer <
For every number from , inclusive, must have a power such
that:
Solving the is considered (but not proven) hard to do in
polynomial time
4. Math : Discrete Logarithm Problem
Solve for , given values , , , and knowing:
Finding is easy if or are known
Quickly solved by brute force if and
What if and ?
5. Math: Discrete Logarithm Problem
Sender starts the exchange and tells Receiver
Privately, Sender chooses and Receiver chooses
Sender computes and tells Receiver the result
Receiver computes and tells Sender the result
Since , Sender can compute
Since , Receiver can compute
Meanwhile, Attacker doesn’t know or and can’t easily derive
6. Concept
• Sender and Receiver derive a shared secret key over a
public channel (no prior arrangements)
• Publicly agree on two public values, and
• Each choose a private value, and
• Use clever math to compute a shared secret key,
• Attackers never overhear enough information to derive the
shared secret key
14. Elgamal Cryptographic System
In 1984, T. Elgamal announced a public key scheme based on discrete
logarithms, closely related to the Diffie – Hellman technique.
