Shared modulus RSA: In an effort to save cost, suppose that Columbia University decides to use a single RSA modulus N for all students on campus. Each student is then given their own $($e$,$ d$)$ pair but not told what $($N$)$ is$.$ Explain why this is insecure. In particular, show that two students with distinct keys $($e$1,$ d$1)$ and $($e$2,$ d$2)$ can easily recover a multiple of $($N$).$ Hint: computing the greatest common divisor $($GCD$)$ using Euclid$$s algorithm is efficient even for huge numbers. $$ Note $1$: Computing any multiple of $($N$)$ is enough to break RSA. Try to see why $$ Note $2$: There are several ways to find $($N$)$ given N and a multiple of $($N$)$ Note $3$: there is actually an algorithm to recover $($N$)$ given only one RSA key pair $($e$,$ d$)$