Exercise 3

Let $N=6$, $p=5$, and $q=16$, and suppose Bob chooses $f(x)=x^{3}+x^{2}-1$ and $g(x)=x^{4}-x^{3}-x+1$. Given $F_{5}(x)=3x^{5}+4x^{4}+x^{3}+2x^{2}+2x+4$ and $F_{16}(x)=7x^{5}+5x^{4}+14x^{3}+9x^{2}+12x+2$, what is Bob’s public key?