Question

3. Alan and Bill agree (through a public exchange) on using the Diffie-Hellman algorithm to create a common secret key. They also agree on two public numbers: q (large prime number), (generator mod q): q = 13, = 3 Alan generates a random RA =11. Bill generates a random RB =13.

(a) What is the SA Alan sends to Bill? (i.e. SA =? (3 points)

(b) What is the SB Bill sends to Alan? (i.e. SB =? (3 points)

(c) Show how Alan can calculate to obtain a common secret key. What is the common secret key?

(4 points) (d) Show how Bill can calculate to obtain a common secret key. What is the common secret key? (5 points)

Note you need to show the calculation procedures step by step in (a)-(d).

Answer 1

We are given the following information :

Large prime number q = 13

Generator g = 3

Random number chosen by Alan RA = 11

Random number chosen by Bill RB = 13

a)

SA = g^RA mod q

SA = 3¹¹ mod 13 = 9

b)

SB = g^RB mod q

SB = 3¹³ mod 13 = 3

c)

Key _Alan = (SB) ^RA mod q

Key _Alan = 3¹¹ mod 13 = 9

The common secret key is 9

d)

Key _Bill = (SA) ^RB mod q

Key _Bill = 9¹³ mod 13 = 9

The common secret key is 9.