Taylor wants to develop a security system for her video streaming service that leverages public

cryptography to protect user accounts. The system operates as follows:

$1.$ When a user joins the service for the first time, they need to register their user ID$,$ denoted

as U $($an integer such as $9876543).$

$2.$ The streaming service has pre$-$configured public and private keys stored securely on the

server.

$3.$ The service generates a secret code $($S$)$ by encrypting U using the service's public key and

sends it to the user$$s email. The user must enter S each time they log in and should keep S

secure$.$

$4.$ During login$,$ the user inputs their user ID $($U$)$ and the received secret code $($S$).$

$5.$ Upon receiving U and S$,$ the streaming service computes a parameter U$\text{'}$ by decrypting S

using the private key.

$6.$ The user is granted access if U equals U$\text{'}.$

Taylor's video streaming service uses the Public$-$Key Cryptography Algorithm to secure user

accounts. Assume you would use your membership number as the user ID U$.$ For example, if your

membership number is $"$M$654321,$ the user ID is U $=654321.$

Answer the following questions:

a$)$ Suppose the streaming service is using the RSA Public$-$Key Cryptography Algorithm. With a

clear description, demonstrate the detailed steps of key generation, secret code S

generation $($i$.$e$.,$ encryption process$),$ and generation of U$\text{'}($i$.$e$.,$ decryption process$).$ Use

parameters: p $=2357$ and q $=2551$ to perform the following:

i$.$ Select a small public key parameter $($e $=65537)$ and show detailed steps to compute

the streaming service$$s public$-$key and private$-$key.

ii$.$ How would the streaming service encrypt user ID U $=$ to produce the secret code S$?$

iii. How would the streaming service decrypt S to produce U