Alice and Bob wish to communicate using RSA cryptography.

Alice selects the two prime numbers $p=13q=7$ and publicises $n=pq=91.$ She also

calculates Euler's phi, $(n),$ and selects an additional integer $e.$

i$)$ What condition must $e$ satisfy?

Alice selects $e=5$ and publicises this.

She also calculates the multiplicative inverse of $e=5$mod$(n).$

ii$)$ Calculate $(n).$

iii$)$ Hence justify that, for $d=29,de-=1$mod$(n).$

iv$)$ Write $e=5$ in binary form.

Bob's message is $m=2.$

v$)$ Show that the message he makes public is $c=m$modn$=32.$

vi$)$ In your own words, clearly explain how Alice decodes Bob's message to recover

$m=2.$ Note, you do not need to calculate the result numerically, but you must

explain the calculations which Alice would need to do$.$