$6.[$S$]$ In DL $($discrete logarithm$)$ based algorithms the private $($secret$)$ key is uniformly selected from the group Zq

$*.$ The public

key is then computed from this private key. Is it feasible to do the opposite, i$.$e$.,$ select the public key uniformly from Zq

$*$and compute the private key? Discuss.

$7.[$S$]$ Consider the RSA experiment on page $332$ of the textbook $($immediately preceding Definition $9\mathrm{.}46).$ One of your

colleagues claims that the adversary must firstly compute d from N$,$ e$,$ and then secondly compute x $=$ yd mod N$.$ Discuss.

$8.[$S$]$ Assume we are using a PKI $($public key infrastructure$)$ based on digital certificates $($which is the norm and practice today$).$

Therefore, we need public$-$key digital signature algorithms, standards and software to this end. One of your colleagues

suggests that digital signatures should suffice and there is no need to have public$-$key encryption standards and software.

Argue that this claim is feasible. Assume that all participants in the system have a digital signature certificate and no other

certificates.

Hint: Consider Diffie$-$Hellman $($DH$)$ Key Exchange including its man$-$in$-$the$-$middle $($MITM$)$ vulnerability.

Plz do not use chat gpt