exploit.py

from Crypto.Util.number import *
from pwn import *

def _encrypt(message):
    r.recvuntil("choice: ")
    r.sendline("1")
    r.recvuntil("encrypt (in hex): ")
    r.sendline(message.encode("hex"))
    ct = r.recvline().strip()[37:].decode("hex")
    r.recvline()
    r.recvline()
    return ct

def extractmod_eknown(_encrypt, e, limit=4):
    """
    Reference: https://crypto.stackexchange.com/questions/43583/deduce-modulus-n-from-public-exponent-and-encrypted-data

    Function to extract the value of modulus, given value of public key exponent

    :input parameters:
    _encrypt : <type 'function'>      : Function interacting with the server for encryption
    e        : <type 'int' or 'long'> : Public Key exponent
    limit    : <type 'int'>           : number of values to be sent for encryption
    """
    try:
        assert limit <= 4
    except AssertionError:
        print "[+] Limit too big!"
        return -1
    try:
        m_list = [2, 3, 5, 7]
        mod_list = [(bytes_to_long(_encrypt(long_to_bytes(m_list[i])))) - (m_list[i]**e) for i in range(limit)]
        _GCD = mod_list[0]
        for i in range(limit):
            _GCD = GCD(_GCD, mod_list[i])
        return _GCD
    except Exception as e:
        print "[+] Exception: ", e

r = process("./run.sh")
N = extractmod_eknown(_encrypt, 65537, 4)
print "N: ", N
assert N != -1
r.sendline("2")
r.recvuntil("modulus: ")
r.sendline(str(N))
print r.recvline().strip()