def problem4(cipher1_b64, cipher2_b64, N1, N2):
cipher1_hex = conversions.b64_to_hex(cipher1_b64)
cipher2_hex = conversions.b64_to_hex(cipher2_b64)
cipher1_b10 = int(cipher1_hex,16)
cipher2_b10 = int(cipher2_hex,16)
common_factor = euclid_etc.euclid(N1, N2)
if (common_factor ==1): #Returning an error as requested if there is no common factor
return "error: there is no common factor"
else:
p1 = N1 / common_factor #N1 = common_factor * p1 N1,N2 are the 2 different moduli
p2 = N2 / common_factor #N2 = common_factor * p2
M1 = (p1 - 1) * (common_factor - 1) #definition of M as in the notes
M2 = (p2 - 1) * (common_factor - 1)
d1 = euclid_etc.extended_euclid(65537, M1)
d2 = euclid_etc.extended_euclid(65537, M2)
d1 = d1[1][0] #Need to access the desired part bc we get a tuple and then a tuple within it in the second (technically [1]) so i need to access the actual wanted part
d2 = d2[1][0] + M2 #Added M2 because I was getting an error bc originally it was negative and we know that a = b(mod n) -> a+n = b(mod n)
plaintext1_b10 = euclid_etc.repeated_squaring(cipher1_b10, d1, N1) #message = c^d(mod n), equation from class and from notes, plug and chug
plaintext2_b10 = euclid_etc.repeated_squaring(cipher2_b10, d2, N2)
plaintext1_hex = hex(plaintext1_b10)
plaintext2_hex = hex(plaintext2_b10)
plaintext1_hex = hex_string_to_hex(plaintext1_hex)
plaintext2_hex = hex_string_to_hex(plaintext2_hex)
plaintext1 = conversions.hex_to_as(plaintext1_hex)
plaintext2 = conversions.hex_to_as(plaintext2_hex)
return (plaintext1, plaintext2) #I returned a tuple of the plaintexts bc I decrypted both of them
def problem1(cipher_b64, N):
cipher_hex = conversions.b64_to_hex(cipher_b64)
cipher_b10 = int(cipher_hex,16)
plaintext_b10 = kthroot(cipher_b10,3)
plaintext_hex_string = hex(plaintext_b10)
plaintext_hex = hex_string_to_hex(plaintext_hex_string)
plaintext_as = conversions.hex_to_as(plaintext_hex)
return plaintext_as
def reduce_git(hashb64, column):
hashhex = conversions.b64_to_hex(hashb64)
hashV = hashhex[:10]
results = []
chars = 'abcdefghijklmnopqrstuvwxyz'
# Cast hash from str to int then decompose into bytes
byteArray = getBytes(hashV)
for i in range(4):
index = byteArray[(i + column) % len(byteArray)]
newChar = chars[index % len(chars)]
results.append(newChar)
return "".join(results)
def problem2(cipher1_b64, cipher2_b64, cipher3_b64, N1, N2, N3):
a1_hex = conversions.b64_to_hex(cipher1_b64)
a2_hex = conversions.b64_to_hex(cipher2_b64)
a3_hex = conversions.b64_to_hex(cipher3_b64)
a1_b10 = int(a1_hex,16)
a2_b10 = int(a2_hex,16)
a3_b10 = int(a3_hex,16)
N2N3inv = euclid_etc.extended_euclid(N2*N3,N1)
N2N3inv = N2N3inv[1][0] #This is all just plug and chug
N1N3inv = euclid_etc.extended_euclid(N1*N3,N2) #into the CRT equation in the
N1N3inv = N1N3inv[1][0] #Lecture notes #7. x = ... see notes for full equation
N1N2inv = euclid_etc.extended_euclid(N1*N2,N3)
N1N2inv = N1N2inv[1][0]
parta = a1_b10 * ((N2N3inv) % N1) * (N3*N2)
partb = a2_b10 * ((N1N3inv) % N2) * (N1*N3)
partc = a3_b10 * ((N1N2inv) % N3) * (N1*N2)
x = (parta + partb + partc) % (N1*N2*N3)
cubeRootx = kthroot(x,3)
x_hex = hex(cubeRootx)
x_hex = hex_string_to_hex(x_hex)
plain = conversions.hex_to_as(x_hex)
return plain
def reduce_git1(hashb64, column):
hashhex = conversions.b64_to_hex(hashb64)
hashV = hashhex
z = b26_to_num('z')
results = []
chars = 'abcdefghijklmnopqrstuvwxyz'
# Cast hash from str to int then decompose into bytes
byteArray = getBytes(hashV)
for i in range(6):
index = byteArray[(i + column) % len(byteArray)]
newChar = chars[index % len(chars)]
results.append(newChar)
"".join(results)
results[3] = num_to_b26((b26_to_num(results[3]) + column) % z, 1)
pword = "".join(results)
return pword
def reduce_git1(hashb64, column):
hashhex = conversions.b64_to_hex(hashb64)
hashV = hashhex
results = []
chars = 'abcdefghijklmnopqrstuvwxyz'
# Cast hash from str to int then decompose into bytes
byteArray = getBytes(hashV)
for i in range(4):
index = byteArray[(i + column) % len(byteArray)]
newChar = chars[index % len(chars)]
results.append(newChar)
letter4 = results[3]
letter4num = ((b26_to_num(letter4)) + column) % 26
newletter4 = num_to_b26(letter4num, 1)
# if column > 100:
# pword = "".join(results)
return "".join(results)
def b64_to_bits(b64text):
text = conversions.b64_to_hex(b64text)
bits = int(text, 16)
return bits