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\( c^d \mod (n) = (m^e)^d \mod (n) = m^{(d*e)} \mod (n) \);

#coding=utf-8
#__author__ = 'ralph'
import random

def extendedGCD(a, b):
    #a*xi + b*yi = ri
    if b == 0:
        return (1, 0, a)
    #a*x1 + b*y1 = a
    x1 = 1
    y1 = 0
    #a*x2 + b*y2 = b
    x2 = 0
    y2 = 1
    while b != 0:
        q = a / b
        #ri = r(i-2) % r(i-1)
        r = a % b
        a = b
        b = r
        #xi = x(i-2) - q*x(i-1)
        x = x1 - q*x2
        x1 = x2
        x2 = x
        #yi = y(i-2) - q*y(i-1)
        y = y1 - q*y2
        y1 = y2
        y2 = y
    return(x1, y1, a)

def computeD(fn, e):
    (x, y, r) = extendedGCD(fn, e)
    #y maybe < 0, so convert it
    if y < 0:
        return fn + y
    return y

def keyGeneration(p,q,e):
    #generate public key and private key
    n = p * q
    fn = (p-1) * (q-1)
    d = computeD(fn, e)
    return (d,n)

p_v = int(raw_input('Please enter the value of p (decimal)\n'))
q_v = int(raw_input('Please enter the value of q (decimal)\n'))
e_v = int(raw_input('Please enter the value of e (decimal)\n'))
c_v = int(raw_input('Please enter the value of ciphertext c (decimal)\n'))

(d,n) = keyGeneration(p_v,q_v,e_v)  #generate d and n

m = pow(c_v,d,n)
print ("The obtained plaintext m is: "+str(m))