a$.$Generate two pairs of Merkle$-$Hellman Knapsack keys, with $2$ different sizes. The size of pair one should be at least $5$ and the size of pair $2$ should be at least $6.$ Justify the selection of all selected numbers.

$[16$ marks: $4$ marks for correct private keys $(2*2=4)$; $2$ marks for justifying the selected numbers; $10$ marks for correct public key including correct calculation steps $(5*2=10)]$

b$.$Use each pair of keys to encrypt and decrypt your full name. You may use the provided Ascii Table $($Appendix A$)$ to convert your name to binary. If you plain test is not multiple of the block size you can add extra zeros at the end of the plain text to make it multiple of the block size.

$[24$ marks: $[8$ marks for correct encryption $(2*4=8)$; $8$ marks multiplicative inverse

calculation $(2*4=8)$; $8$ marks for correct decryption $(2*4=8)]$