This python program will allow you to see how RSA works!

RSA Tester.py

import random
import math
import Queue

def isPrime(n):
  if n == 2 or n == 3: return True
  if n < 2 or n%2 == 0: return False
  if n < 9: return True
  if n%3 == 0: return False
  r = int(n**0.5)
  f = 5
  while f <= r:
    if n%f == 0: return False
    if n%(f+2) == 0: return False
    f +=6
  return True

def gcd (m, n):
    while (m != n):
      if (m > n):
        m = m - n
      else:
        n = n - m
    return m

def isCoPrime (a, b):
    if (gcd(a, b) != 1):
      return True
    else:
      return False

def extended_gcd(aa, bb):
    lastremainder, remainder = abs(aa), abs(bb)
    x, lastx, y, lasty = 0, 1, 1, 0
    while remainder:
        lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
        x, lastx = lastx - quotient*x, x
        y, lasty = lasty - quotient*y, y
    return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)

def modInverse(m, a):
	g, x, y = extended_gcd(a, m)
	if g != 1:
		raise ValueError
	return x % m

def encrypt(m):
    c=(m**myE) % myN
    return c

def decrypt(c):
    m=(c**myD) % myN
    return m


print ("RSA Tester by Theodore Messinezis")
print ("Written in Python. This code is open-source!")
print ("This program will allow you to test the crypto algorithm created by Rivest, Shamir, and Adleman (RSA).")
print ("This version of RSA uses 1 byte / 8 bit prime random numbers.")
raw_input('Press <Enter> to run the RSA crypto algorithm\n-----------------------------------------------------------------------------------------------------\n')
while True:
    primeA = random.randint(128,255)
    if isPrime(primeA ):
        break
print ("First 8 bit prime found:\n   " + str(primeA) + " | " + str("{0:b}".format(primeA)))
while True:
    primeB = random.randint(128,255)
    if primeA!=primeB and isPrime(primeB):
        break
print ("Second 8 bit prime found:\n   " + str(primeB) + " | " + str("{0:b}".format(primeB)))
myN = primeA * primeB
print ("N = " + str(primeA) + " * " + str(primeB) +" =\n   " + str(myN) + " | " + str("{0:b}".format(myN)))
myF = (primeA-1) * (primeB-1)
print ("f(" + str(myN) + ") = "+ str(primeA-1) + " * " + str(primeB-1) + " :\n   " + str(myF) + " | " + str("{0:b}".format(myF)))
while True:
    myE = random.randint(2,myF-1)
    if isPrime(myE) and (not isCoPrime(myE, myF)):
        break
print ("Non co-prime to f(N) and prime found E:\n   " + str(myE) + " | " + str("{0:b}".format(myE)))
myD = modInverse(myF,myE)
print ("Modular multiplicative inverse found to be D:\n   " + str(myD) + " | " + str("{0:b}".format(myD)))
print
messageNew = "Test Message"
ASCIIString = ""
for myChar in messageNew:
    ASCIIString += str(ord(myChar)) + ", "

ASCIIString = ASCIIString[:-2]
print ("To encrypt message '" + messageNew + "' with public key = (N,E):\n  Message '" + messageNew + "' to numbers = " + ASCIIString)

CipherString = ""
q = Queue.Queue()
for myChar in messageNew:
    cipher=encrypt(ord(myChar))
    CipherString += str(cipher) + ", "
    q.put(cipher)
CipherString = CipherString[:-2]
print ("  Cipher is now: " + CipherString)
print ("\nTo decrypt cipher private key = (D)")

newMessageString = ""
myMessageNew = ""
for myChar in messageNew:
    myCipher = q.get()
    message=decrypt(myCipher)
    newMessageString += str(message) + ", "
    myMessageNew+=chr(message)
newMessageString = newMessageString[:-2]

print ("  Message is now: " + newMessageString)

print ("  Translated with ASCII: " + myMessageNew)

print ("\n-----------------------------------------------------------------------------------------------------\n")
messageNew = raw_input("Enter your message to encrypt: ")
ASCIIString = ""
for myChar in messageNew:
    ASCIIString += str(ord(myChar)) + ", "

ASCIIString = ASCIIString[:-2]
print ("To encrypt message '" + messageNew + "' with public key = (N,E):\n  Message '" + messageNew + "' to numbers = " + ASCIIString)

CipherString = ""
q = Queue.Queue()
for myChar in messageNew:
    cipher=encrypt(ord(myChar))
    CipherString += str(cipher) + ", "
    q.put(cipher)
CipherString = CipherString[:-2]
print ("  Cipher is now: " + CipherString)
print ("\nTo decrypt cipher private key = (D)")

newMessageString = ""
myMessageNew = ""
for myChar in messageNew:
    myCipher = q.get()
    message=decrypt(myCipher)
    newMessageString += str(message) + ", "
    myMessageNew+=chr(message)
newMessageString = newMessageString[:-2]

print ("  Message is now: " + newMessageString)

print ("  Translated with ASCII: " + myMessageNew)
print ("\n-----------------------------------------------------------------------------------------------------")
print("Press <Enter> to quit")
raw_input()