Question

Alice's public key for a DH key exchange is (p,g)=(1103,554) and

her private key is a=800. If Bob's private key is b=400, what does
Bob transmit to Alice in order to set up a private key using DH?

Answer 1

Bob will transmit his computed public value using the Diffie-Hellman key exchange algorithm to Alice. He calculates this by raising the shared base to the power of his private key mod the prime number, resulting in 554^400 mod 1103.

Step-by-step explanation:

The question asks about the process of establishing a private key between Alice and Bob using the Diffie-Hellman (DH) key exchange algorithm. In this cryptographic method, both participants have their own private keys and a shared public key-set. The shared public key-set is denoted as (p, g), where p is a prime number and g is a primitive root modulo p. Alice's private key is denoted as a, and Bob's private key is denoted as b.

To engage in the DH key exchange, Bob must compute his public value to transmit to Alice. To do this, he calculates gb mod p, using his private key b and the shared base g. Given Bob's private key b = 400, the prime number p = 1103, and the base g = 554, Bob's transmission to Alice would be calculated as follows:

Bob's Public Value (to transmit) = 554400 mod 1103

This computation will yield Bob's public value, which he will then send to Alice. Alice will perform a similar computation using her private key, and both parties will arrive at the same secret shared key by using the respective public values they have exchanged.