Exercise $1$: RSA Encryption

$1\mathrm{.}1.$ Explain the RSA Encryption Algorithm

Write a brief explanation of the RSA encryption$/$decryption algorithm, highlighting the key steps involved.

Describe the role of the public key and private key in RSA encryption.

Explain the concept of prime numbers and their significance in RSA.

$1\mathrm{.}2.$ Calculation of RSA Parameters

Ahmed and Fahd want to communicate and keep the message between them confidential using RSA encryption.

Key generation

Ahmed chooses two prime numbers: $p=17$ and $q=11.$

Calculate the value of $n,(n)$ and put $e=13$ for Ahmed's public key.

Calculate Ahmed's private key.

Encryption

Fahd wants to send a plaintext message: "SECRET" to Ahmed. He converts the plaintext into numeric representation using a predetermined mapping $(A=1,B=2,C=3$ and so on$).$ Then, he encrypts the numeric representation of the message using Ahmed's public key $($e$,n).$

Show the step$-$by$-$step encryption process $($use your Windows scientific calculator to perform the calculations accurately$).$

Decryption

Ahmed receives another encrypted message from Fahd: $"943713313353".$

Show the step$-$by$-$step decryption process $($use your Windows scientific calculator to perform the calculations accurately$).$