In your favorite language (preferable in Python) create the following functions:MRT => Use Miller-Rabin Primality Test to choose a prime number with s=512 bits and check the primality test.EA => Use...

In your favorite language (preferable in Python) create the following functions:

1. 
   

   
   MRT
   
   =>
   
   Use Miller-Rabin Primality Test to choose a prime number with s=512 bits and check the primality test.
   

   
   


2. 
   

   
   EA
   
   
   =>
   
   Use Euclidean Algorithm to evaluate gcd
   

   
   


3. 
   

   
   EEA
   
   
   =>
   
   Use Extended Euclidean Algorithm to find modular inverse of the value
   

   
   


4. 
   

   
   powmod_sm
   
   =>
   
   Square and multiply algorithm to evaluate exponentiation.
   

   
   

Now write the code for

1. 
   

   
   RSA Key Generation (use above functions 1., 2., 3. ) should be
   

   
   




1. 
   

   
   Choose two primes
   
   p
   
   and
   
   q
   
   of
   
   s
   
   bits using
   
   MRT
   
   where
   
   p
   
   is not equal to
   
   q
   .
   

   
   


2. 
   

   
   Calculate
   
   n=p*q
   , and
   
   ϕ(n) = (p-1)*(q-1)
   

   
   


3. 
   

   
   Chose randomly e from the set of {1,…,
   
   ϕ
   n
   -1
   } and check using EA if
   
   gcd(e, ϕ(n))=1
   
   if not chosen again until it fulfills the condition.
   

   
   


4. 
   

   
   Calculate
   
   d=
   e
   -1
   
   mod ϕ(n)
   
   using EEA. Note that
   
   d
   
   should be at least
   
   0.3*s
   
   bits
   

   
   


5. 
   

   
   Output
   
   k
   Pub
   =(n,e)
   
   and
   
   k
   Pr
   
   = (d)
   

   
   




2. 
   

   
   RSA Encryption with input
   
   k
   Pub
   =(n,e)
   
   and random plaintext
   
   x
   
   and output should be ciphertext
   
   y
   , evaluate exponentiation using the function
   
   powmod_sm
   
   

   
   


3. 
   

   
   RSA Decryption with input
   
   k
   Pr
   
   = (d)
   
   and ciphertext
   
   y
   
   and output should be plaintext
   
   x
   , evaluate exponentiation using the function
   
   powmod_sm
   . Please make sure to check that you get the same plaintext value before the encryption.
   

   
   

Please write your report and include a snapshot of output with you source code.