Problem $1$: You were assigned specific values $p,q,$ and e$.$ If not, see me before$/$after class.

$($a$)$

Input your p$,$ q$,$ and e below. Ensure that these are correct.

$p=231$

$q=455$

$e=21023$

$($This e is not Euler's Number here or anywhere else in the project!$)$

$($b$)$

Let $n=pq$ and input the numeric values of $n$ and $(n)($The Euler Phi Function$)$

$($c$)$ Write down the definition of $E(x)$ according to your assigned values. Substitute numeric values for $e$ and $n$ where appropriate.

$E(x)=$

Use the $^$ symbol to indicate exponentiation. Do not include parentheses or commas.

$($d$)$ Compute $,$ e$)$ using the Extended Euclidean Algorithm below. Replace $(n)$ and e with the correct numeric values below.

Leave unused cells blank. The last row should contain the GCD$,$ and values $x$ and y such that $gcd((n),e)=ax+by$ where $a=(n)$ and $b=e.$

From your results, compute $d,$ the inverse of e as a reduced residue modulo n$),$ i$.$e

$d=$

$($Remember to reduce the result modulo $(n)$ if necessary!$)$

To check your work, verify that de $-=1(mod(n))$

Remember to replace $(n)$ and e with the actual numbers.

Make sure to verify your results before you submit!!!

Complete every column, including the index column!

Some unused rows at the end may be blank.