Write a program that will verify the following steps outlining the RSA encryption$/$decryption

technique using the prescribed test values:

i$.$ Choose two prime numbers p and q consisting of exactly $7$ digits.

ii$.$ Compute N $=$ pq$.$ The security of RSA depends on not making p and q publicly known

even though N will be made public. If N can be factored, then RSA becomes insecure.

iii. Compute $$ $($N $)=($p $1)($q $1)($given that p and q are prime, $($N $)$ is easily

computed by using $($p $1)($q $1)$ where p and q are known only to you$).$

iv$.($Key Generation$)$ Choose a small prime number e such that $1<$ e $<$ $($N $)$ and

gcd$($e$,$ $)=1.$ Use the extended Euclidean algorithm to compute d such that ed

mod $=1($make sure you verify that gcd$($e$,$ $)=1).$ After the algorithm runs do

not forget to convert your result to a positive answer d mod $.$

a$.$ Public Key: $($N$,$ e$)$

b$.$ Private Key: $($N$,$ d$)$

v$.$ Encode the plaintext $$STOP$$ into two blocks m$1$m$2$ of four digits using the UTF$-8$ code:

m$1=8384,$ m$2=7980.$

vi$.($Encryption$)$ For each plaintext block, use the repeated squaring algorithm to encrypt

the plaintext message m into the ciphertext c by computing

c $=$ me mod N

vii. $($Decryption$)$ Use the repeated squaring algorithm to decrypt the ciphertext back into

the plaintext message by computing

m $=$ cd mod N