# PicoCTF 2k14 - Low Entropy

# cat low_entropy.py
import Crypt
import gmpy
import Socket

publickey = 0xc20a1d8b3903e1864d14a4d1f32ce57e4665fc5683960d2f7c0f30d5d247f5fa264fa66b49e801943ab68be3d9a4b393ae22963888bf145f07101616e62e0db2b04644524516c966d8923acf12af049a1d9d6fe3e786763613ee9b8f541291dcf8f0ac9dccc5d47565ef332d466bc80dc5763f1b1139f14d3c0bae072725815f
ciphertext = 0x49f573321bdb3ad0a78f0e0c7cd4f4aa2a6d5911c90540ddbbaf067c6aabaccde78c8ff70c5a4abe7d4efa19074a5249b2e6525a0168c0c49535bc993efb7e2c221f4f349a014477d4134f03413fd7241303e634499313034dbb4ac96606faed5de01e784f2706e85bf3e814f5f88027b8aeccf18c928821c9d2d830b5050a1e

cont = True

while cont:
 s = Socket.Socket(Socket.TCP)
 s.connect('vuln2014.picoctf.com', 51818)
 s.read()
 recv = s.read()
 if recv != '':
  n = int('0x' + recv, 16)
  p = Crypt.egcd(publickey, n)[0]
  if p != 1:
   cont = False
 s.close()

q = publickey / p
n = p * q
totien = (p - 1) * (q - 1)
e = 65537
d =  gmpy.invert(e, totien)
cleartext = pow(ciphertext, d, n)

print hex(cleartext)[2:].decode('hex')

# python low_entropy.py
[i] Sock: Connecting...
[i] Sock: Connecting...
[i] Sock: Connecting...
[i] Sock: Connecting...
Good thing no one can read this! I'd hate for them to know that the flag is make_sure_your_rng_generates_lotsa_primes.