Question

Alice and Bob agree to use the prime p = 941 and the primitive root g = 627. Alice chooses the secret key a = 347.Similarly, Bob chooses the secret key b = 781. Compute the shared secret key. ​

Answer 1

Answer: 470 is the Shared Secret key.

Explanation:

Alice and Bob agree to use the prime p = 941 and the  primitive root g = 627. Alice chooses the secret key a = 347 and computes  A = 390 ≡ 627347 (mod 941).

Similarly, Bob chooses the secret key b = 781  and computes B = 691 ≡ 627781 (mod 941).

Then Alice and Bob are both able to compute the number  470 ≡ $627^{347.781}$ ≡ $A^{b}$   ≡ $B^{a}$ (mod 941),  so 470 is their shared secret.