Important: Solve it in an octave programming language. $($write for me the code please$)$

Here is the question:

Implementing RSA Encryption and Decryption.

Pseudocode for RSA Encryption and Decryption

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Inputs:

p$,$ q: small prime numbers

plaintext: word to be encrypted and decrypted $($plaintext will be converted to UPPERCASE$)$

Outputs:

Display of public and private keys

Encrypted & Decrypted Codes

Decrypted text

$------------------------------------------------------------------------------------------$

PSEUDOCODE

Initialize RSA Parameters

Compute n$=$p$$q$,$

Compute $($ n $)=($p$1)($q$1)$

Select Public Exponent

Select e to an initial smallest odd number $($start $11,13,...)$ such that

gcd$($e$,($ n $)=1$ if not, choose the next odd number

Compute Private Key d using the Extended Euclidean Algorithm to find

d$,$ the modular inverse of e modulo $($ n $),$ such that d$$e $1($mod $($ n $)).$

$[$Call function: $=$ extended$\_$gcd$($a$,$ b$)]$

Display Public and Private Keys

Print the public key $($e$,$ n$).$

Print the private key $($d$,$ n$).$

Convert Plaintext to ASCII Codes $($use UPPERCASE$)$

Encrypt Plaintext $[$call the function: mod$\_$exp$($base$,$ e$,$ n$)]$

Display the ciphered Code.

Decrypt the ciphered Code. $[$call the function: mod$\_$exp$($base$,$ d$,$ n$)]$

Display the decrypted ciphered Code

Display Decrypted Text

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see sample outputs below

For example:

Test data:

p $=11$ ;

q $=17$;

plaintext $=\text{'}$HI$\text{'}$;

RSArun$($p$,$q$,$plaintext$)$

Result:

Public key $($e$,$ n$)$: $(11,187)$

Private key $($d$,$ n$)$: $(131,187)$

A$->$Z $[$A$=>0,..$Z$=>25]$: $7273$

Ciphered Code: $14962$

Decrypted Code: $7273$

Decrypted text: HI

$-----------------------------------------------------------$

Test data:

p $=23$;

q $=11$;

plaintext $=\text{'}$BP$\text{'}$;

RSArun$($p$,$q$,$plaintext$)$

Result:

Public key $($e$,$ n$)$: $(13,253)$

Private key $($d$,$ n$)$: $(17,253)$

A$->$Z $[$A$=>0,..$Z$=>25]$: $6680$

Ciphered Code: $198247$

Decrypted Code: $6680$

Decrypted text: BP

$-----------------------------------------------------------$

Test data:

p $=61$;

q $=53$;

plaintext $=$ 'MATH';

RSArun$($p$,$q$,$plaintext$)$

Result:

Public key $($e$,$ n$)$: $(11,3233)$

Private key $($d$,$ n$)$: $(851,3233)$

A$->$Z $[$A$=>0,..$Z$=>25]$: $77658472$

Ciphered Code: $7572811278350$

Decrypted Code: $77658472$

Decrypted text: MATH