Question

Suppose that your friend Ayesha wants to share a secret number with you via the DiffieHellmann key exchange. Ayesha selected the prime number p = 23 and the primitive root g = 10. (For this problem, you do not have to verify that 10 is a primitive root mod 23.) (a) You have selected your private number b = 4. What number should you send to Ayesha? (b) Ayesha has selected her private number (which she keeps secret) and has sent you the number A = 11. What is the secret number s that you have shared with Ayesha?

Answer 1

Hi,

According to the theorem a) we have selected private number b=4. The formula for the public key is $G^{b}$ mod P.

so we have to share $10^{4}$ mod 23 = 19 .

The number we share is 19.

b) The shared secret would be shared key A to the power our private number b modulo 23

$11^{4}$ mod 23 =14

if Ayesha wants to calculate the shared key she will do the same we are sharing 19. so she will do $19^{as}$ mod 23 here as is Ayesha's private number which will also be equal to 14 according to the theorem

Thank you