In a Diffie-Hellman Key Exchange, Alice and Bob have chosen prime value q = 19 and primitive root a = 10. If Alice's secret key is 4 and Bob's secret key is 6, determine the following three values:

a. The value Alice sends to Bob.
b. The value Bob sends to Alice
c. The shared key they exchanged. For this part, you need to show only how either Alice or Bob computed the shared key. You do not need to show both computations.

a) 6

b) 11

c) 11

Explanation:

Given

Prime value q =n= 19

primitive root (a) =10

Alice secret key = 4

Bob secret key = 6

a) The value Alice Sends to Bob

aPrivate key of Alice mod n

= 10^4 mod 19

= 10000 mod 19

=6

b)The value Bob sends to Alice

aPrivate key of Bob mod n

= a3 mod n

= 10^6 mod 19

=1000000 mod 19

= 11

c)

Both the parties calculate the value of secret key at their respective side.

secret key obtained by Alice

= 11

secret key obtained by Bob

= 11

Finally, both the parties obtain the same value of secret key.

The value of common secret key = 17

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