$2($a$)$ Alice's ElGamal public key $(p,g,g^x$ modp$)$ is $(23,11,9).$ Obtain

her private key by brute force. What does having Alice's private

key allow you to do$?$ How can Alice better protect her private key?

$($b$)$ Calculate the load factor of the hash table below. Given that the

load factor is quite high, what would you recommend to reduce

the number of collisions? Show how the values $583,629$ and

$975$ would be inserted using

i$.$ Linear probing

ii$.$ Quadratic probing

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Summer $2022$

$($c$)$ Draw the directed unweighted graph represented by the

adjacency matrix below. Show how i$)$ a depth$-$first and ii$)$ a

breadth$-$first search would traverse the graph starting at A$.$