Diffie-Hellman Key Exchange Algorithm

Diffie-Hellman Key Exchange Algorithm

Introduction

The Diffie Hellman algorithm widely known as Key exchange algorithm or key agreement algorithm developed by Whitefield Diffie and Martin Hellman in 1976. The purpose of the algorithm is to enable two users to securely exchange a key that can be used for subsequent encryption of messages. The algorithm itself is limited to the exchange of secret values.

Diffie – Hellman Key Exchange Algorithm steps:

Step-1: Select q (prime number) and α (α is primitive root of q)

Step-2: User A Key Generation: select X_A, X_A < q

Calculate public key Y_A, Y_A = α^X_A mod q

YA Shared with user B

Step-3: User B Key Generation: select X_B, X_B < q

Calculate public key Y_B, Y_B = α^X_B mod q

YB shared with user A

Step-4: Calculation of secret key by user A: K = (Y_B)^X_A mod q

Step-5: Calculation of secret key by user B: K = (Y_A)^X_B mod q

 

Same Secret key generate both sides

K = (Y_B) ^X_A mod q

    = (α^X_B mod q) ^X_A mod q

    = (α^X_B) ^X_A mod q

    = (α^X_A) ^X_B mod q

    = (α^X_A mod q) ^X_B mod q

            = (Y_A) ^X_B mod q

    = K

 

Diffie – Hellman Key Exchange Algorithm explain with example:

Step – 1: Select q (prime number) and α (α is primitive root of q)

Example, here q = 7, α = 17.

 

Step – 2: User A Key Generation: Select X_A < q,

calculate public key Y_A and shared with user B: Y_A = α^X_A mod q

Example, Here X_A = 6,

Calculate Y_A = α^X_A mod q ⇒17⁶ mod 7 ⇒ 1

 

Step – 3: User B Key Generation: Select X_B < q,

calculate public key Y_B and shared with user A: Y_B = α^X_B mod q

Example, Here X_B = 4,

Calculate Y_B = α^X_B mod q ⇒17⁴ mod 7 ⇒ 4

 

Step – 4: Calculation of secret key by user A:

K = (Y_B) ^X_A mod q

Example, Here Y_B = 4, X_A = 6

Calculate K = (Y_B) ^X_A mod q ⇒4⁶ mod 7 ⇒ 1

 

Step – 5: Calculation of secret key by user B:

K = (Y_A) ^X_B mod q

Example, Here Y_A = 1, X_B = 4

Calculate K = (Y_A) ^X_B mod q ⇒1⁴ mod 7 ⇒ 1

 

Solution of exercise (Given in video)

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