def decrypt(filename, private, p, q):
decrypted = []
## Open file and get the contents
encrypted = openFile(filename, False)
## Using the chinese remainder theorem
## pCRT = C^d mod p
## qCRT = C^d mod q
pCRT, qCRT = [], []
for block in encrypted:
pCRT.append(pow(block, private[0], p))
qCRT.append(pow(block, private[0], q))
## Geting bitvector versions of the p * q values for their multiplicative inverses
pBV = BitVector(intVal=p)
qBV = BitVector(intVal=q)
## Xp = q * (q^-1 mod p)
## Xq = p * (p^-1 mod q)
pX = q * int(qBV.multiplicative_inverse(pBV))
qX = p * int(pBV.multiplicative_inverse(qBV))
## C^d mod n = (VpXp + VqXq) mod n
for i in range(len(encrypted)):
decrypted.append(((pCRT[i] * pX) + (qCRT[i] * qX)) % private[1])
return decrypted
def GenerateKeys(eVAL):
## Setup the prime generator
pg = PrimeGenerator(bits=128, debug=0)
while (True):
p = pg.findPrime()
q = pg.findPrime()
## Check p and q are different
if p == q: continue
## Check left two MSB's are 1 (bin command returns 0b appended at front)
if not (bin(p)[2] and bin(p)[3] and bin(q)[2] and bin(q)[3]): continue
## Check that the totients of p and q are co-prime to e
if (GCD(p - 1, eVAL) != 1) or (GCD(q - 1, eVAL) != 1): continue
break
## Calculate modulus
n = p * q
## Calculate totient of n
tn = (p - 1) * (q - 1)
modBV = BitVector(intVal=tn)
eBV = BitVector(intVal=eVAL)
## Calculate multiplicative inverse
d = eBV.multiplicative_inverse(modBV)
d = int(d)
## Create public and private sets
public, private = [eVAL, n], [d, n]
## Return items
return public, private, p, q, eVAL
def generate_private_key_d(e, p, q):
n = p * q
phi = (p - 1) * (q - 1)
bv_modulus = BitVector(intVal=phi)
bv = BitVector(intVal=e)
bv_result = bv.multiplicative_inverse(bv_modulus)
d = int(bv_result)
return d
def decrypt_chinese_remainder(cipher_blocks, e, p, q):
d = generate_private_key_d(e, p, q)
d_p = d % (p - 1)
d_q = d % (q - 1)
bv_modulus = BitVector(intVal=p)
q_bv = BitVector(intVal=q)
q_inv = int(q_bv.multiplicative_inverse(bv_modulus))
decrypted = []
for c in cipher_blocks:
m1 = (c**d_p) % p
m2 = (c**d_q) % q
h = (q_inv * (m1 - m2)) % p
m = m2 + (h * q)
decrypted.append(m)
return decrypted
# RSA block cipher
import sys
from BitVector import BitVector
# P, Q generated using modified PrimeGenerator.py
# PrimeGenerator.py was modified to generate prime-1 coprime e
p = 332302551650268460897954734536272420319
q = 258222644969751264151459428110328891689
e = 65537
# d = 51045946630242965074234865575892110109352763218080182137347987188415402400657
bv_p = BitVector(intVal=p)
bv_q = BitVector(intVal=q)
bv_pi = bv_p.multiplicative_inverse(bv_q)
bv_qi = bv_q.multiplicative_inverse(bv_p)
pi = int(bv_pi) # p inverse mod q
qi = int(bv_qi) # q inverse mod p
n = p * q
bv_n = BitVector(intVal=n)
tn = (p - 1) * (q - 1)
bv_tn = BitVector(intVal=tn)
bv_e = BitVector(intVal=e)
bv_d = bv_e.multiplicative_inverse(bv_tn)
d = int(bv_d)
def mod_exp(a, b, n):
result = 1
while(b > 0):
# ECE 404 HW #6
# RSA block cipher
import sys
from BitVector import BitVector
# P, Q generated using modified PrimeGenerator.py
# PrimeGenerator.py was modified to generate prime-1 coprime e
p = 332302551650268460897954734536272420319
q = 258222644969751264151459428110328891689
e = 65537
# d = 51045946630242965074234865575892110109352763218080182137347987188415402400657
bv_p = BitVector(intVal=p)
bv_q = BitVector(intVal=q)
bv_pi = bv_p.multiplicative_inverse(bv_q)
bv_qi = bv_q.multiplicative_inverse(bv_p)
pi = int(bv_pi) # p inverse mod q
qi = int(bv_qi) # q inverse mod p
n = p * q
bv_n = BitVector(intVal=n)
tn = (p - 1) * (q - 1)
bv_tn = BitVector(intVal=tn)
bv_e = BitVector(intVal=e)
bv_d = bv_e.multiplicative_inverse(bv_tn)
d = int(bv_d)
def mod_exp(a, b, n):
result = 1
