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| from pwn import *
from sage.all import *
import ast
from Crypto.Util.number import bytes_to_long, long_to_bytes
import sys
sys.path.append('./MT19937-Symbolic-Execution-and-Solver-master/source')
from MT19937 import MT19937, MT19937_symbolic
from tqdm import trange
import itertools
context.log_level = 'error'
def main():
r = process(['sage', 'task.sage'])
r.recvuntil(b'p =')
p = int(r.recvline().strip())
from sage.parallel.multiprocessing_sage import pyprocessing
def find_ab_worker(*args):
p, attempts = args
import random
for _ in range(attempts):
a = random.randint(1, p-1)
b = random.randint(1, p-1)
try:
E1 = EllipticCurve(Zmod(p), [a, b])
E2 = EllipticCurve(Zmod(p), [a+b, a-b])
E1o = E1.order()
E2o = E2.order()
except:
continue
m1 = prod(list(filter(lambda x: x < 2 ** 32,
(base ** exp for base, exp in factor(E1o)))))
m2 = prod(list(filter(lambda x: x < 2 ** 32,
(base ** exp for base, exp in factor(E2o)))))
ml1 = m1.bit_length()
ml2 = m2.bit_length()
if ml1 > 40 and ml2 > 40 and (ml1 + ml2) > 120:
return (a, b)
return None
def find_ab(p, processes=20, batch_size=2):
parallel_iter = pyprocessing(processes)
P = parallel(p_iter=parallel_iter)
while True:
inputs = [((p, batch_size), {}) for _ in range(processes) ]
results = list(P(find_ab_worker)(inputs))
for res in results:
if res[1] is not None:
return res[1]
a, b = find_ab(p)
r.sendlineafter(b'a =', str(a).encode())
r.sendlineafter(b'b =', str(b).encode())
r.recvuntil(b'A =')
A_data = r.recvline().strip().decode()
AP, AQ = ast.literal_eval(A_data)
r.recvuntil(b'enc =')
enc_data = r.recvline().strip().decode()
enc_points = ast.literal_eval(enc_data)
P_xy, Q_xy, encP_xy, encQ_xy = enc_points
E1 = EllipticCurve(GF(p), [a, b])
E2 = EllipticCurve(GF(p), [a+b, a-b])
P = E1(*P_xy)
Q = E2(*Q_xy)
encP = E1(*encP_xy)
encQ = E2(*encQ_xy)
known = AP + AQ[:45]
data = []
for i in known:
for _ in range(5):
data.append(i & 2**32-1)
i >>= 32
data = data[:624]
try:
rng = MT19937(state_from_data = (data, 32))
except:
r.close()
return None
for tryrev in trange(80, 300):
rng = MT19937(state_from_data = (data, 32))
rng.reverse_states(tryrev)
m_list = [rng() >> 30 for _ in range(tryrev)]
s = []
for i in m_list:
if i <= 1:
s.append(i)
if len(s) == 80:
break
E1o = E1.order()
E2o = E2.order()
def dl(Q, P, n, filnum):
primes = list(filter(lambda x: x < 2 ** 32 and gcd(x, filnum) == 1, (base ** exp for base, exp in factor(n))))
dlogs = []
for fac in primes:
t = int(n) // int(fac)
dlog = discrete_log(t*Q,t*P,operation="+")
dlogs.append(dlog)
k = int(crt(dlogs,primes))
return k, prod(primes)
sAP = sum([s[i]*AP[i] for i in range(80)])
sAQ = sum([s[i]*AQ[i] for i in range(80)])
sum_AP, modA = dl(encP, P, E1o, sAP)
sum_AQ, modB = dl(encQ, Q, E2o, sAQ)
mA = sum_AP * pow(sAP, -1, modA) % modA
mB = sum_AQ * pow(sAQ, -1, modB) % modB
try:
m = crt([mA, mB], [modA, modB])
return m, lcm(modA, modB)
except:
print('FUCK')
return (mA, modA) if modA > modB else (mB, modB)
if __name__ == '__main__':
flags = []
modulos = []
for _ in trange(1000):
res = main()
if res is not None:
if res[0] is not None and res[1] is not None:
flags.append(int(res[0]))
modulos.append(int(res[1]))
print("flags =", flags)
print("modulos =", modulos)
lst = list(zip(flags, modulos))
result = []
for i in range(2, len(lst)+1):
for combo in itertools.combinations(lst, i):
result.append(list(combo))
for combo in result:
f, m = map(list, zip(*combo))
try:
flag = long_to_bytes(crt(f, m))
if flag.startswith(b'flag'):
print(flag)
exit()
except Exception as e:
pass
|
