def keyMaker(p, q, k):
#Checking if inputs are prime
if cryptoMath.gcd(p, q) != 1:
return None
rsaModulus = p * q
euilersToitent = (p - 1) * (q - 1)
e = 1
for i in range(euilersToitent - 1, 1, -1):
if cryptoMath.gcd(i, rsaModulus) == 1:
e = i
break
# Public Key = rsaModulus and e
d = (k * euilersToitent + 1) // e
return [[e, rsaModulus], [d, rsaModulus]]
def generateKey(keySize):
# Creates a public/private key pair with keys that are keySize bits in
# size. This function may take a while to run.
# Step 1: Create two prime numbers, p and q. Calculate n = p * q.
print('Generating p prime...')
p = rabinMiller.generateLargePrime(keySize)
print('Generating q prime...')
q = rabinMiller.generateLargePrime(keySize)
n = p * q
# Step 2: Create a number e that is relatively prime to (p-1)*(q-1).
print('Generating e that is relatively prime to (p-1)*(q-1)...')
while True:
# Keep trying random numbers for e until one is valid.
e = random.randrange(2 ** (keySize - 1), 2 ** (keySize))
if cryptoMath.gcd(e, (p - 1) * (q - 1)) == 1:
break
# Step 3: Calculate d, the mod inverse of e.
print('Calculating d that is mod inverse of e...')
d = cryptoMath.findModInverse(e, (p - 1) * (q - 1))
publicKey = (n, e)
privateKey = (n, d)
print('Public key:', publicKey)
print('Private key:', privateKey)
return (publicKey, privateKey)
def hackAffine(message):
print 'Hacking...'
# Python programs can be stopped at any time by pressing
# Ctrl-C (on Windows) or Ctrl-D (on Mac and Linux)
print '(Press Ctrl-C or Ctrl-D to quit at any time.)'
# brute-force by looping through every possible key
for key in range(len(affineCipher.SYMBOLS)**2):
keyA = affineCipher.getKeyParts(key)[0]
if cryptoMath.gcd(keyA, len(affineCipher.SYMBOLS)) != 1:
continue
decryptedText = affineCipher.decryptMessage(key, message)
if not SILENT_MODE:
print 'Tried Key %s: ... (%s)' % (key, decryptedText[:40])
if detectEnglish.isEnglish(decryptedText):
# Check with the user if the decrypted key has been found.
print ''
print 'Possible encryption hack:'
print 'Key: %s' % (key)
print 'Decrypted message: ' + decryptedText[:200]
print ''
print 'Enter D for done, or just press Enter to continue hacking:'
response = raw_input('> ')
if response.strip().upper().startswith('D'):
return decryptedText
return None
def getRandomKey():
while True:
keyA = random.randint(2, len(SYMBOLS))
keyB = random.randint(2, len(SYMBOLS))
if cryptoMath.gcd(keyA, len(SYMBOLS)) == 1:
return keyA * len(SYMBOLS) + keyB
def generateKey(self):
# Creates a public/private key pair with keys that are keySize bits in
# size. This function may take a while to run.
# Step 1: Create two prime numbers, p and q. Calculate n = p * q.
print('Generating p prime...')
p = rabinMiller.generateLargePrime(self.keySize)
print('Generating q prime...')
q = rabinMiller.generateLargePrime(self.keySize)
n = p * q
# Step 2: Create a number e that is relatively prime to (p-1)*(q-1).
print('Generating e that is relatively prime to (p-1)*(q-1)...')
while True:
# Keep trying random numbers for e until one is valid.
e = random.randrange(2**(self.keySize - 1), 2**(self.keySize))
if cryptoMath.gcd(e, (p - 1) * (q - 1)) == 1:
break
# Step 3: Calculate d, the mod inverse of e.
print('Calculating d that is mod inverse of e...')
d = cryptoMath.modinv(e, (p - 1) * (q - 1))
self.publicKey = (n, e)
self.privateKey = (n, d)
print('Public key:', self.publicKey)
print('Private key:', self.privateKey)
print()
def generateKey(keySize):
p = 0
q = 0
print('Generating p prime...')
while p == 1:
p = primeNum.generaeLargePrime(keySize)
q = primeNum.generaeLargePrime(keySize)
n = p * q
print('Generating e that is relatively prime to (p - 1) * (q - 1)...')
while True:
e = random.randrange(2 ** (keySize - 1), 2 ** (keySize))
if cryptoMath.gcd(e, (p - 1) * (q - 1)) == 1:
break
print('Calculating d that is mod inverse of e...')
d = cryptoMath.findModInverse(e (p - 1) * (q - 1))
publicKey = (n, e)
privateKey = (n, d)
print('Public key:', publicKey)
print('Private key:', privateKey)
return(publicKey, privateKey)
def hackAffine(message):
print 'Hacking...'
# Python programs can be stopped at any time by pressing
# Ctrl-C (on Windows) or Ctrl-D (on Mac and Linux)
print '(Press Ctrl-C or Ctrl-D to quit at any time.)'
# brute-force by looping through every possible key
for key in range(len(affineCipher.SYMBOLS) ** 2):
keyA = affineCipher.getKeyParts(key)[0]
if cryptoMath.gcd(keyA, len(affineCipher.SYMBOLS)) != 1:
continue
decryptedText = affineCipher.decryptMessage(key, message)
if not SILENT_MODE:
print 'Tried Key %s: ... (%s)' % (key, decryptedText[:40])
if detectEnglish.isEnglish(decryptedText):
# Check with the user if the decrypted key has been found.
print ''
print 'Possible encryption hack:'
print 'Key: %s' % (key)
print 'Decrypted message: ' + decryptedText[:200]
print ''
print 'Enter D for done, or just press Enter to continue hacking:'
response = raw_input('> ')
if response.strip().upper().startswith('D'):
return decryptedText
return None
def checkKeys(keyA, keyB, mode):
if keyA == 1 and mode == 'encrypt':
sys.exit('The affine cipher becomes incredibly weak when key A is set to 1. Choose a different key.')
if keyB == 0 and mode == 'encrypt':
sys.exit('The affine cipher becomes incredibly weak when key B is set to 0. Choose a different key.')
if keyA < 0 or keyB < 0 or keyB > len(SYMBOLS) - 1:
sys.exit('Key A must be greater than 0 and Key B must be between 0 and %s.' % (len(SYMBOLS) - 1))
if cryptoMath.gcd(keyA, len(SYMBOLS)) != 1:
sys.exit('Key A (%s) and the symbol set size (%s) are not relatively prime. Choose a different key.' % (keyA, len(SYMBOLS)))
def main():
multi = MultiplicativeCipher(104729,13)
cipherText = multi.encrypt("this is a super awesome year '2000' message!!!")
print(cipherText)
for i in range(95):
for j in range(95):
if cryptoMath.gcd(i,95) == 1:
multi.setKeys(i,j)
decoded = multi.decrypt(cipherText)
print(decoded)
def main():
multi = MultiplicativeCipher(104729, 13)
cipherText = multi.encrypt(
"this is a super awesome year '2000' message!!!")
print(cipherText)
for i in range(95):
for j in range(95):
if cryptoMath.gcd(i, 95) == 1:
multi.setKeys(i, j)
decoded = multi.decrypt(cipherText)
print(decoded)
def checkKeys(keyA, keyB, mode):
if keyA == 1 and mode == 'encrypt':
sys.exit('Cipher is weak if key A is 1. Choose a different key.')
if keyB == 0 and mode == 'encrypt':
sys.exit('Cipher is weak if key B is 0. Choose a different key.')
if keyA < 0 or keyB < 0 or keyB > len(SYMBOLS) - 1:
sys.exit(
'Key A must be greater than 0 and Key B must be between 0 and %s.'
% (len(SYMBOLS) - 1))
if cryptoMath.gcd(keyA, len(SYMBOLS)) != 1:
sys.exit(
'Key A (%s) and the symbol set size (%s) are not relatively prime. \n Choose a different Key.'
% (keyA, len(SYMBOLS)))
def generateKey(keySize):
p = 0
q = 0
while p == q:
p = primeNum.generateLargePrime(keySize)
q = primeNum.generateLargePrime(keySize)
n = p * q
while True:
e = random.randrange(2**(keySize - 1), 2**keySize)
if cryptoMath.gcd(e, (p - 1) * (q - 1)) == 1:
break
d = cryptoMath.findModInverse(e, (p - 1) * (q - 1))
publicKey = (n, e)
privateKey = (n, d)
return publicKey, privateKey
def checkKeys(keyA, keyB, mode):
if keyA == 1 and mode == 'encrypt':
sys.exit(
'The affine cipher becomes incredibly weak when key A is set to 1. Choose a different key.'
)
if keyB == 0 and mode == 'encrypt':
sys.exit(
'The affine cipher becomes incredibly weak when key B is set to 0. Choose a different key.'
)
if keyA < 0 or keyB < 0 or keyB > len(SYMBOLS) - 1:
sys.exit(
'Key A must be greater than 0 and Key B must be between 0 and %s.'
% (len(SYMBOLS) - 1))
if cryptoMath.gcd(keyA, len(SYMBOLS)) != 1:
sys.exit(
'Key A (%s) and the symbol set size (%s) are not relatively prime. Choose a different key.'
% (keyA, len(SYMBOLS)))
def createKey(keysize):
p = 0
q = 0
e = 0
d = 0
print('finding p, q, and n')
while q == p:
q = primeNum.generateLargePrime(keysize=1024)
p = primeNum.generateLargePrime(keysize=1024)
n = p * q
print('finding e')
while cryptoMath.gcd(e, (p - 1) * (q - 1)) != 1:
e = random.randrange(2**(keysize - 1), 2**(keysize))
print('finding d')
d = cryptoMath.findModInverse(e, (p - 1) * (q - 1))
publicKey = (n, e)
privateKey = (n, d)
return (publicKey, privateKey)
def hackAffine(message):
print('Hacking...')
for key in range(len(affineCipher.SYMBOLS) ** 2):
keyA = affineCipher.getKeyParts(key)[0]
if cryptoMath.gcd(keyA, len(affineCipher.SYMBOLS)) != 1:
continue
decryptedText = affineCipher.decryptMessage(key, message)
if not SILENT_MODE:
print('Tried key %s... (%s)' % (key, decryptedText[:40]))
if detectEnglish.isEnglish(decryptedText):
print()
print('Possible encryption hack:')
print('Key: %s' % (key))
print('Decrypted message: ' + decryptedText[:200])
response = input('>')
if response.strip().upper().startswith('D'):
return decryptedText
return None
def getRandomKey():
while True:
keyA = random.randint(2, len(SYMBOLS))
keyB = random.randint(2, len(SYMBOLS))
if cryptoMath.gcd(keyA, len(SYMBOLS)) == 1:
return keyA * len(SYMBOLS) + keyB
# This program proves that the keyspace of the affine cipher is limited
# to len(SYMBOLS) ^ 2.
import affineCipher, cryptoMath
message = 'Make things as simple as possible, but not simpler.'
for keyA in range(2, 100):
key = keyA * len(affineCipher.SYMBOLS) + 1
if cryptoMath.gcd(keyA, len(affineCipher.SYMBOLS)) == 1:
print(keyA, affineCipher.encryptMessage(key, message))