from cStringIO import StringIO

flag = "l0w_n"

def modx(base,exp,mod):
    r = 1;
    while (exp > 0):
        if (exp % 2 == 1):
            r = (r * base) % mod
        base = (base * base) % mod
        exp = exp/2
    return r

def probprime(s):
    if s%2==0:
        s += 1
    smolprimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
    while len(set([modx(i,s-1,s) for i in smolprimes])) != 1 or modx(2,s-1,s) != 1:
        s+=2
    return(s)

def get_problem(random):
    # add Probable Prime function later
    p = probprime(random.randint(10**20,9*10**20))
    q = probprime(random.randint(10**20,9*10**20))
    e = 65537
    salt = "".join([random.choice("0123456789abcdef") for i in range(4)])
    return (p, q, e, salt)

def generate_ciphertext(random):
    p, q, e, salt = get_problem(random)
    encoded = int(("flag{%s_%s}" % (flag, salt)).encode('hex'),16)
    ciphertext =  'n: '+str(p*q)+'\n'
    ciphertext += 'e: '+str(e)+'\n'
    ciphertext += 'c: '+str(pow(encoded, e, p*q))+'\n'

    return StringIO(ciphertext)

def generate(random):
    return dict(files={
        "ciphertext2.txt": generate_ciphertext
    })

def grade(random, key):
    p, q, e, salt = get_problem(random)
    if key.find("%s_%s" % (flag, salt)) >= 0:
        return True, "Correct!"
    return False, "Nope."