Problem Set $3$: Diffie$-$Hellman Key Exchange

Part A:

$1.$ Scenario:

You are tasked with helping two users, Alice and Bob, securely establish a shared secret key using Diffie$-$Hellman.

$2.$ Given Values:

$-$ Prime Number $($P$)$: $23$

$-$ Generator $($G$)$: $5$

$-$ Alice's Private Key $($a$)$: $8$

$-$ Bob's Private Key $($b$)$: $15$

$3.$ Tasks: Compute the symmetric key for both Alice and Bob.

Part B:

Question: Comparison Between RSA and Diffie$-$Hellman:

$-$ Explain the key differences between RSA and Diffie$-$Hellman in terms of:

$-$ Purpose $($Encryption vs$.$ Key Exchange$)|$

$-$ Security $($Use of private$/$public keys$)$

$-$ Algorithm process $($Asymmetric encryption vs$.$ shared secret generation$)$

$-$ Why might you choose Diffie$-$Hellman over RSA in some scenarios?

Provide examples of practical use cases for each algorithm.