class BreakEncryption:
#Constructor for BreakEncryption class
def __init__(self, objCommon):
try:
self.common = objCommon
self.encryption = Encryption(objCommon)
self.keyGeneration = KeyGeneration(objCommon)
self.decryption = Decryption(objCommon)
except Exception as ex:
print(
"An error occurred while initializing class BreakEncryption. Error: ",
ex)
#String Representation
def __str__(self):
return "No member variables other than member objects to classes"
#4. Break encryption and get original message using Baby Step Giant Step algorithm
def BreakEncryptionGetMessage(self):
try:
print("\nIf your listening to somebody's conversation as a Man In The Middle",\
"and wish to break an encrypted message,")
print(
"you must have the knowledge of encrypted message and the header sent to the Reciever."
)
#Read Encrypted Message and Header from the file
tupleEncMsgHead = self.encryption.ReadEncryptedMessageAndHeader()
if len(tupleEncMsgHead) > 0:
print(
"\nThe public key of the Receiver is required to break an encryption."
)
print(
"The Public Keys are usually publicly available via Key Hosting Services."
)
#Read public key from file
receiversKeys = self.keyGeneration.ReadReceiversKeys(False)
if len(receiversKeys) > 0:
encryptedMessage, header = tupleEncMsgHead[
0], tupleEncMsgHead[1]
primitiveElement = receiversKeys[0]
primitiveRaisedSecretModPrime = receiversKeys[1]
randomPrime = receiversKeys[2]
print(
"\nBreaking Encyption (using Baby Step Giant Step Algorithm)..."
)
self.__PerformBabyStepGiantStep(
encryptedMessage, header, primitiveElement,
primitiveRaisedSecretModPrime, randomPrime)
except Exception as ex:
print(
"An error occurred in function BreakEncryption.BreakEncryptionGetMessage while processing. Error: ",
ex)
#To perform Baby-Step-Giant-Step algorithm using Receiver's public keys and Header to break Encryption
# and get the original message
def __PerformBabyStepGiantStep(self, encryptedMessage, header,
primitiveElement,
primitiveRaisedSecretModPrime, randomPrime):
try:
randomVar = self.__ComputePowerVariable(header, primitiveElement,
randomPrime)
#print("randomVar:", randomVar)
if randomVar == -1:
print(
"\nBaby Step Giant Step failed to break encryption for given Public Key and Header combination."
)
print(
"Please try again for a different Receiever\'s Public Key and Header combination..."
)
else:
#Encrypted Message = message * (c^b mod p) mod p
#message = Encrypted Message * Inverse of (c^b mod p) mod p
#c^b mod p
primitiveRaisedSecRaisedRandomModPrime = self.common.GetExponentiation(
primitiveRaisedSecretModPrime, randomVar, randomPrime)
#print("primitiveRaisedSecRaisedRandomModPrime:", primitiveRaisedSecRaisedRandomModPrime)
#message = Encrypted Message * Inverse of (c^b mod p) mod p
message = (encryptedMessage *
self.decryption.GetInverseModPrime(
primitiveRaisedSecRaisedRandomModPrime,
randomPrime)) % randomPrime
print("\nCracked Original Message:", message)
except Exception as ex:
print(
"An error occurred in function BreakEncryption.__PerformBabyStepGiantStep while processing. Error: ",
ex)
#In the equation a = b ^ c mod n, below function computes 'c'
# Representationally: answerVar = baseVar ^ powerVar Mod prime
def __ComputePowerVariable(self, answerVar, baseVar, prime):
try:
dictLHS, dictRHS = {}, {}
m = int(math.ceil(math.sqrt(prime - 1)))
#print("m:", m)
invBaseVar = self.decryption.GetInverseModPrime(baseVar, prime)
#print("invBaseVar:", invBaseVar)
invBaseVarRaisedm = self.common.GetExponentiation(
invBaseVar, m, prime)
#print("invBaseVarRaisedm:", invBaseVarRaisedm)
#answerVar * (invBaseVar ^ m) ^ i = baseVar ^ j
#where 0 <= i <=m
#and 0 <= j < m
#All L.H.S. values of equation answerVar * (invBaseVar ^ m) ^ i = baseVar ^ j
for i in range(m + 1):
valueLHS = (self.common.GetExponentiation(
invBaseVarRaisedm, i, prime) * answerVar) % prime
dictLHS[i] = valueLHS
#All R.H.S. values of equation answerVar * (invBaseVar ^ m) ^ powerVar = baseVar ^ otherPowerVar
for j in range(m):
valueRHS = self.common.GetExponentiation(baseVar, j, prime)
dictRHS[j] = valueRHS
listCombinationTuple = [(i, j) for i in dictLHS for j in dictRHS
if dictLHS[i] == dictRHS[j]]
#print("listCombinationTuple:", listCombinationTuple)
if len(listCombinationTuple) > 0:
powerVar = int((listCombinationTuple[0][0] * m) +
listCombinationTuple[0][1])
else:
#Baby-Step-Giant-Step algorithm failed to crack encryption
powerVar = -1
#print("powerVar:", powerVar)
return powerVar
except Exception as ex:
print(
"An error occurred in function BreakEncryption.__ComputePowerVariable while processing. Error: ",
ex)
class Decryption:
#Constructor for Decryption function
def __init__(self, objCommon):
try:
self.common = objCommon
self.keyGeneration = KeyGeneration(objCommon)
self.encryption = Encryption(objCommon)
except Exception as ex:
print(
"An error occurred while initializing class Decryption. Error: ",
ex)
#String Representation
def __str__(self):
return "common: " + str(self.common) + ", keyGeneration: " + str(
self.keyGeneration) + ", encryption: " + str(self.encryption)
#3. Decrypt an encrypted message using your (Receiver's) Private Key
def DecryptMessage(self):
try:
#Read Encrypted Message and Header from file
tupleEncMsgHead = self.encryption.ReadEncryptedMessageAndHeader()
if len(tupleEncMsgHead) > 0:
#Read keys from file
receiversKeys = self.keyGeneration.ReadReceiversKeys(True)
if len(receiversKeys) > 0:
encryptedMessage, header = tupleEncMsgHead[
0], tupleEncMsgHead[1]
#primitiveElement = receiversKeys[0]
#primitiveRaisedSecretModPrime = receiversKeys[1]
randomPrime = receiversKeys[2]
privateKey = receiversKeys[3]
#Calculating Header ^ PrivateKey Mod p
#where header = (g^b mod p)
#So, mathematically the formula can be written as (g^b mod p) ^a mod p
headerRaisedEncMsgModPrime = self.common.GetExponentiation(
header, privateKey, randomPrime)
#Calculating inverse of Header ^ PrivateKey Mod p
invHeaderRaisedEncMsgModPrime = self.GetInverseModPrime(
headerRaisedEncMsgModPrime, randomPrime)
decryptedMessage = (invHeaderRaisedEncMsgModPrime *
encryptedMessage) % randomPrime
print("\nDecrypted Original Message:", decryptedMessage)
except Exception as ex:
print(
"An error occurred in function Decryption.DecryptMessage while processing. Error: ",
ex)
#To perform extended euclidean to help find the inverse mod prime
def PerformExtendedEuclidean(self, element, prime):
try:
if prime == 0:
return [element, 1, 0]
vals = self.PerformExtendedEuclidean(prime, element % prime)
d = vals[0]
a = vals[2]
b = vals[1] - (element // prime) * vals[2]
return [d, a, b]
except Exception as ex:
print(
"An error occurred in function Decryption.PerformExtendedEuclidean while processing. Error: ",
ex)
#To calculate Inverse of an element mod prime
def GetInverseModPrime(self, element, prime):
try:
vals = self.PerformExtendedEuclidean(element, prime)
if vals[1] < 0:
inverse = prime + vals[1]
else:
inverse = vals[1]
return inverse
except Exception as ex:
print(
"An error occurred in function Decryption.GetInverseModPrime while processing. Error: ",
ex)
