Diffie-Hellman Key Exchange Algorithm, Example

1. PCIT303: Cryptography and Information Security
Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
(An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NACC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Information Technology
(UG Programme - NBAAccredited)
Dr. M.A. Jawale
Professor and Head, Dept. of IT

2. Unit II : Cryptography
▪ Diffie-Hellman Key Exchange Algorithm
▪ Example
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

3. Diffie-Hellman Key Exchange Algorithm
▪ A simple public-key algorithm is Diffie-Hellman key exchange. This protocol enables
two users to establish a secret key using a public-key scheme based on discrete
logarithms.
▪ The protocol is secure only if the authenticity of the two participants can be
established.
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

4. Continue….
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

5. Continue….
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

6. Example
▪ q = 353 prime number
▪ Primitive root of 353, here α = 3
▪ A and B select secret keys XA = 97 and XB = 233 respectively
▪ A computes YA = 397 mod 353 = 40
▪ B computes YB = 3233 mod 353 = 248
▪ After they exchange public keys, each can compute the common secret key
▪
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

7. Diffie-Hellman Key Exchange
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

8. Man-in-the-Middle Attack
▪ The protocol depicted in above Figure is insecure against a man-in-the-middle attack.
▪ Suppose Alice and Bob wish to exchange keys, and Darth is the adversary. The attack
proceeds as follows.
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

9. Continue….
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

10. Continue….
▪ At this point, Bob and Alice think that they share a secret key, but instead Bob and
Darth share secret key K1 and Alice and Darth share secret key K2.
▪ All future communication between Bob and Alice is compromised in the following
way
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

11. Continue….
▪ The key exchange protocol is vulnerable to such an attack because it does not
authenticate the participants. This vulnerability can be overcome with the use of
digital signatures and public-key certificates.
▪
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

12. Reference
1. William Stallings, “Cryptography and Network Security Principles and
Practice”, Fourth Edition, Chapter 10.
Unit-II: Part-IV Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology