Implement RSA Algorithm Encryption and Decryption in Python.

• RSA (Rivest–Shamir–Adleman) is an algorithm used by modern computers to encrypt and decrypt messages. 
• It is an asymmetric cryptographic algorithm. 
• Asymmetric means that there are two different keys. 
• This is also called public key cryptography, because one of the keys can be given to anyone.

EXAMPLE :-

import math

print("RSA ENCRYPTION/DECRYPTION")
print("*****************************************************")

# Input Prime Numbers
print("PLEASE ENTER THE 'x' AND 'y' VALUES BELOW:")
x = int(input("Enter a prime number for x: "))
y = int(input("Enter a prime number for y: "))
print("*****************************************************")

def prime_check(k):
    if (k == 2):
        return True
    elif ((k < 2) or ((k % 2) == 0)):
        return False
    elif (k > 2):
        for i in range(2, k):
            if not (k % i):
                return false
    return True


check_x = prime_check(x)
check_y = prime_check(y)
while (((check_x == False) or (check_y == False))):
    x = int(input("Enter a prime number for x: "))
    y = int(input("Enter a prime number for y: "))
    check_x = prime_check(x)
    check_y = prime_check(y)

n = x * y
print("RSA Modulus(n) is:", n)

r = (x - 1) * (y - 1)
print("Eulers Toitent(r) is:", r)
print("*****************************************************")

def egcd(e, r):
    while (r != 0):
        e, r = r, e % r
    return e

def eugcd(e, r):
    for i in range(1, r):
        while (e != 0):
            a, b = r // e, r % e
            if (b != 0):
                print("%d = %d*(%d) + %d" % (r, a, e, b))
            r = e
            e = b

def eea(a, b):
    if (a % b == 0):
        return (b, 0, 1)
    else:
        gcd, s, t = eea(b, a % b)
        s = s - ((a // b) * t)
        print("%d = %d*(%d) + (%d)*(%d)" % (gcd, a, t, s, b))
        return (gcd, t, s)

def mult_inv(e, r):
    gcd, s, _ = eea(e, r)
    if (gcd != 1):
        return None
    else:
        if (s < 0):
            print("s=%d. Since %d is less than 0, "
                  "s = s(modr), i.e., s=%d." % (s, s, s % r))
        elif (s > 0):
            print("s=%d." % (s))
        return s % r

for i in range(1, 1000):
    if (egcd(i, r) == 1):
        e = i
print("The value of e is:", e)
print("*****************************************************")

print("RSA ALGORITHM:")
eugcd(e, r)
print("END OF THE STEPS USED TO ACHIEVE EUCLID'S ALGORITHM.")
print("*****************************************************")
print("RSA EXTENDED ALGORITHM:")
d = mult_inv(e, r)
print("END OF THE STEPS USED TO ACHIEVE THE VALUE OF 'd'.")
print("The value of d is:", d)
print("*****************************************************")
public = (e, n)
private = (d, n)
print("Private Key is:", private)
print("Public Key is:", public)
print("*****************************************************")

def encrypt(pub_key, n_text):
    e, n = pub_key
    x = []
    m = 0
    for i in n_text:
        if (i.isupper()):
            m = ord(i) - 65
            c = (m ** e) % n
            x.append(c)
        elif (i.islower()):
            m = ord(i) - 97
            c = (m ** e) % n
            x.append(c)
        elif (i.isspace()):
            spc = 500
            x.append(500)
    return x


def decrypt(priv_key, c_text):
    d, n = priv_key
    txt = c_text.split(',')
    x = ''
    m = 0
    for i in txt:
        if (i == '500'):
            x += ' '
        else:
            m = (int(i) ** d) % n
            m += 65
            c = chr(m)
            x += c
    return x

message = input("You like Encrypted or Decrypted?
                (Separate numbers with ',' for Decryption):")
print("Your Message is ::", message)

choose = input("Type '1' for Encryption and '2' for Decryption.")

if (choose == '1'):
    enc_msg = encrypt(public, message)
    print("Your Encrypted Message is:", enc_msg)
    print("Thank you for using the RSA Encryption Algorithm. Goodbye!")

elif (choose == '2'):
    print("Your Decrypted Message is:", decrypt(private, message))
    print("Thank you for using the RSA Encryption Algorithm. Goodbye!")

else:
    print("You entered the wrong option.")
    print("Thank you for using the RSA Encryption Algorithm. Goodbye!")

OUTPUT

RSA ENCRYPTION/DECRYPTION
*****************************************************
PLEASE ENTER THE 'x' AND 'y' VALUES BELOW:
Enter a prime number for x: 3
Enter a prime number for y: 5
*****************************************************
RSA Modulus(n) is: 15
Eulers Toitent(r) is: 8
*****************************************************
The value of e is: 999
*****************************************************
RSA ALGORITHM:
8 = 0*(999) + 8
999 = 124*(8) + 7
8 = 1*(7) + 1
END OF THE STEPS USED TO ACHIEVE EUCLID'S ALGORITHM.
*****************************************************
RSA EXTENDED ALGORITHM:
1 = 8*(1) + (-1)*(7)
1 = 999*(-1) + (125)*(8)
s=-1. Since -1 is less than 0, s = s(modr), i.e., s=7.
END OF THE STEPS USED TO ACHIEVE THE VALUE OF 'd'.
The value of d is: 7
*****************************************************
Private Key is: (7, 15)
Public Key is: (999, 15)
*****************************************************
You like Encrypted or Decrypted? (Separate numbers with ',' for Decryption):3,15,20,17,13
Your Message is :: 3,15,20,17,13
Type '1' for Encryption and '2' for Decryption.2
Your Decrypted Message is: MAFIH
Thank you for using the RSA Encryption Algorithm. Goodbye!