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import random
import math
def RSA_cles():
minPrime = 0
maxPrime = 500
cached_primes = [i for i in range(minPrime, maxPrime) if check_if_prime(i)]
p = random.choice([i for i in cached_primes])
q = random.choice([i for i in cached_primes])
if p==q :
RSA_cles()
if not check_if_prime(p):
print("Error p not prime")
return {}
elif not check_if_prime(q):
print("Error q not prime")
return {}
else:
try:
n = p*q
phi = (p-1)*(q-1)
(e,d) = find_e_d(phi)
keys = {}
keys["cle_publique"] = {"e":e,"n":n}
keys["cle_privee"] = {"d":d,"p":p,"q":q}
except :
keys = {'cle_publique': {'e': 115, 'n': 21389}, 'cle_privee': {'d': 2011, 'p': 73, 'q': 293}}
return keys
def encode_private(private_key, message):
d = private_key["d"]
p = private_key["p"]
q = private_key["q"]
n = p*q
numbers = [ord(d) for d in str(message)]
res = ''
for num in numbers:
M = int(num)
m = M**d % n
res += str(m) + ' '
return res
def decode_public(public_key, message):
e = public_key["e"]
n = public_key["n"]
numbers = message.split()
res = ''
for num in numbers:
m = int(num)
M = m**e % n
res += chr(M)
return res
def encode_public(cle_publique, message):
e = cle_publique["e"]
n = cle_publique["n"]
numbers = message.split()
res = ''
for num in numbers:
m = int(num)
M = m**e % n
res += str(M) + ' '
return res
def decode_private(cle_privee, message):
d = cle_privee["d"]
p = cle_privee["p"]
q = cle_privee["q"]
n = p*q
numbers = message.split()
res = ''
for num in numbers:
M = int(num)
m = M**d % n
res += str(m) + ' '
return res
def transform_word_into_numbers(word):
res = ''
for char_index in range(len(word)):
num = ord(word[char_index])
res += str(num) + ' '
print(word + " is written as " + res)
return res
def transform_numbers_into_word(string_of_numbers):
numbers = string_of_numbers.split()
res = ''
for num in numbers:
char = chr(int(num))
res += char
print(string_of_numbers + " gives as word " + res)
return res
def find_e_d(phi):
i = random.randint(7,15)
mul = phi*i+1
divisors = get_divisors(mul)
if len(divisors) <= 2:
return find_e_d(phi)
else:
j = random.randint(2, len(divisors)-1)
e = divisors[j]
d = mul/e
return (int(e),int(d))
def check_if_prime(n):
for i in range(2, n):
if (n % i) == 0:
return False
return True
def get_divisors(n):
div = []
i = 1
while i <= math.sqrt(n):
if (n % i == 0):
if (n / i == i):
div.append(i)
else:
div.append(i)
div.append(n/i)
i = i + 1
return div
if __name__ == "__main__":
keys = RSA_cles()
print(keys)
public = keys["cle_publique"]
private = keys["cle_privee"]
word = "We did IT!! "
word_as_number = transform_word_into_numbers(word)
message_coded = encode_public(public, word_as_number)
message_decoded = decode_private(private, message_coded)
number_as_word = transform_numbers_into_word(message_decoded)