In this problem, you will implement the RSA cryptosystem in Python, the most popular public$-$key cryptosystem used for secure data transmission. Remember that you need four parameters to implement this $(\backslash ($ p$,$ q$,$ e $\backslash )$ and $\backslash ($ d $\backslash ))$ as explained in the class.

Things to do:

$1.$ Prime Number Selection:

$-$ You are given a text file 'primes.txt$\text{'}$ that contains prime numbers between $100$ and $1000.$

$-$ Randomly select two prime numbers p and q from this file.

$2.$ RSA Key Generation:

$-$ Write a function rsa$\_$keygen.

$-$ Calculate $\backslash (\backslash$mathrm$\{$n$\}=\backslash$mathrm$\{$p$\}^\{*\}\backslash$mathrm$\{$q$\}\backslash ),$ where n is the modulus for both the public and private keys.

$-$ Calculate Euler's Totient function, $\backslash (\backslash$varphi$($n$)=($p$-1)*($q$-1)\backslash ).$

$-$ Set $\backslash (\backslash$mathbf$\{=\}7\backslash ).$

$-$ Compute the private key d using the Extended Euclidean Algorithm $(\backslash ($ d $\backslash$equiv e$^\{\backslash$wedge$\}(-1)\backslash$bmod $\backslash$phi$($n$)\backslash )).$ A sample python method $($ExEuclid$.$py$)$ for the Extended Euclidean Algorithm is included in the assignment where the output x represents d $($See this $\backslash (\backslash$underline$\{$l i n k$\}\backslash )$ for explanation$).$

$3.$ Encryption

$-$ Write a function rsa$\_$encrypt that converts each character of the plaintext "Computer" to its ASCII value $($May use ord $()$ in Python$).$

$-$ Calculate the Ciphertext: $\backslash ($ C$=$M$^\{$e$\}\backslash$bmod n $\backslash )$

$4.$ Decryption

$-$ Write a function rsa$\_$decrypt that calculates the Plaintext: $\backslash ($ M$=$C$^\{$d$\}\backslash$bmod n $\backslash )$

$-$ Convert the decrypted ASCII values back to characters to recover the original message.

$5.$ Displaying Results

$-$ Display the generated public and private keys.

$-$ Show the encrypted and decrypted version of the plaintext "Computer".

Additional Notes:

$-$ You may not use built$-$in Python RSA or Stream Cipher implementations.

$-$ You may write helper functions$/$methods if needed. For example, you may need to write a function to calculate the totient value for RSA.

$-$ Use good coding practice. Use comments to make your code readable.