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 problem7(p, g, gx_mod_p, firstComponent, first_secondComponent, m, second_secondComponent):
m_hex = conversions.as_to_hex(m)
m_b10 = int(m_hex,16)
gxy = euclid_etc.extended_euclid(m_b10,p)
gxy = gxy[1][0]
gxy = (first_secondComponent * gxy) % p
gxy_inverse = euclid_etc.extended_euclid(gxy, p)
gxy_inverse = gxy_inverse[1][0]
plaintext_b10 = (gxy_inverse * second_secondComponent) % p
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 problem3(ct, d, modulus):
# modulus = 118655596447903224963869613053944974689306948978385022351313547236325408711597515968013120482999812623684614237188826586513936280546323473924322265897469916282911780567243884859836121621708694140679468147474220271417145483116948895892297437839699778114403528270801117190611396069302409336194794071895031049811
# d = 23731119289580644992773922610788994937861389795677004470262709447265081742319503193602624096599962524736922847437765317302787256109264694784864453179493978848181776281125630457673065339633910037899644296946114786385008468034547208885433370715974640426127989454209067113013826578800440508863151210816724921125
# ct = 'LbJFbZa7eoMEQE8uPICTjzxFqvtM2qLPf6OSNOR6bgIJ8IlSWMMIOL4s7qevd77GRtLTz6EgC38EVjbp+ZHKJ5inX582MlxjD6WYcqGEYOnvCFGBpeFJnkAvhFIWxNyIx1tk1xxQgTHU8wMHjq/rMCl6USuZcSH4L1bzUMmgfZE='
a = random.randint(1, modulus-1)
e = 5
k = e * d - 1
while pow(a, k, modulus) == 1 and k % 2 == 0:
k = k / 2
r = pow(a, k, modulus)
if pow(r, 2, modulus) == 1:
xy = euclid_etc.extended_euclid(r-1, modulus)
p = xy[0]
q = modulus/p
m = (p-1)*(q-1)
d_new = modinv(3, m)
decrypt_me = kthroot(3, d_new)
ct_as_bits = b64_to_bits(ct)
convert_me = pow(ct_as_bits, d_new, modulus)
h = hex(convert_me)
h = h[2:-1]
answer = conversions.hex_to_as(h)
print answer
return answer
else:
problem3(ct, d, modulus)
def problem4(ct1_b64, ct2_b64, N1, N2):
# def problem4():
# N1 = 87750187518907655534583445808737942078016029371855217057442341331127022016930461105786023716013285380470222803872626192434912740863485532564125627646878636545449869643527771922181597178447982975143657375859594541373428795038041796818858805812228886812351199020336314262507362189851970680226889619203804537151
# N2 = 59077605606399909603607705484000546044333045357566473814158491087439387780574866766800852465743470772146755309189078604396507686696592563062056700875467732286553829707195406383141965288479916793429869646143662227281782900822010619445408818002981548245734527538573941174294649831309213962935858200869524073603
# ct1_b64 = 'Ur/BIau7ZZBdwxD8P3xDJFJGMfkJDXNU5rbY7GlvlRkGae4NEMo3pMq9r8Jk2akGSj47SZ00L+eTmeMIIfis3RoG7jjBdj03p5lLtgrLwnjP0lzr31fasl5+NVZIvmnoEt56Figi54lIAXEj4ig06MHFG2KfotLYJTnwabangS4='
# ct2_b64 = 'CPEXorDgegEqM6UttzFLaccAN/t4QB1FTDS+NL3TSofQlq3Rs/BebbNn4Qj/Vo4FmTwV3P0+n+hlIhjXzOgEgdgV3BmiBE3rIBHqUc+q0FoVvWJU1+jvFpEeellYZMX8vG7O9us5JKfDAHjPaHWZSwv++BSX4rh+5O01flxzlJA='
xy = euclid_etc.extended_euclid(N1, N2)
p = xy[0]
q1 = N1/p
q2 = N2/p
m1 = (p-1)*(q1-1)
m2 = (p-1)*(q2-1)
d1 = modinv(65537, m1)
d2 = modinv(65537, m2)
ct1_as_bits = b64_to_bits(ct1_b64)
ct2_as_bits = b64_to_bits(ct2_b64)
pt1_as_bits = pow(ct1_as_bits, d1, N1)
pt2_as_bits = pow(ct2_as_bits, d2, N2)
h1 = hex(pt1_as_bits)
h2 = hex(pt2_as_bits)
h1 = h1[2:-1]
h2 = h2[2:-1]
answer1 = conversions.hex_to_as(h1)
answer2 = conversions.hex_to_as(h2)
print answer1
print answer2
return 'done'
def problem8(p, g, gx_mod_p, firstComponent, secondComponent, y):
gxy = euclid_etc.repeated_squaring(gx_mod_p, y, p)
plaintext = euclid_etc.extended_euclid(gxy, p)
plaintext_b10 = plaintext[1][0]
plaintext_b10 = (plaintext_b10 * secondComponent) % p
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 problem6(p, g, gx_mod_p, x, firstComponent, secondComponent):
gxy = euclid_etc.repeated_squaring(firstComponent,x,p) #gxy = g^xy (mod p)
plaintext = euclid_etc.extended_euclid(gxy,p)
plaintext = plaintext[1][0] #Just like problem 4, need to get the desired part
plaintext_b10 = (plaintext * secondComponent) % p
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 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