import random
from secret import flag
from fractions import Fraction

def score(a,b):
    if abs(a-b)<1/2**10:
        # capping score to 1024 so you dont get extra lucky
        return Fraction(2**10)
    return Fraction(2**53,int(2**53*a)-int(2**53*b))

total_score = 0
for _ in range(2000):
    try:
        x = random.random()
        y = float(input('enter your guess:\n'))
        round_score = score(x,y)
        total_score+=float(round_score)
        print('total score: {:0.2f}, round score: {}'.format(
            total_score,round_score))
        if total_score>10**6:
            print(flag)
            exit(0)
    except:
        print('Error, exiting')
        exit(1)
else:
    print('Maybe better luck next time')

#This class from https://github.com/icemonster/symbolic_mersenne_cracker
"""
MIT License

Copyright (c) 2021 icemonster

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
"""

from z3 import *
from random import Random
from itertools import count
import time
import logging

logging.basicConfig(format='STT> %(message)s')
logger = logging.getLogger()
logger.setLevel(logging.DEBUG)

SYMBOLIC_COUNTER = count()

class Untwister:
    def __init__(self):
        name = next(SYMBOLIC_COUNTER)
        self.MT = [BitVec(f'MT_{i}_{name}', 32) for i in range(624)]
        self.index = 0
        self.solver = Solver()

    #This particular method was adapted from https://www.schutzwerk.com/en/43/posts/attacking_a_random_number_generator/
    def symbolic_untamper(self, solver, y):
        name = next(SYMBOLIC_COUNTER)

        y1 = BitVec(f'y1_{name}', 32)
        y2 = BitVec(f'y2_{name}' , 32)
        y3 = BitVec(f'y3_{name}', 32)
        y4 = BitVec(f'y4_{name}', 32)

        equations = [
            y2 == y1 ^ (LShR(y1, 11)),
            y3 == y2 ^ ((y2 << 7) & 0x9D2C5680),
            y4 == y3 ^ ((y3 << 15) & 0xEFC60000),
            y == y4 ^ (LShR(y4, 18))
        ]

        solver.add(equations)
        return y1

    def symbolic_twist(self, MT, n=624, upper_mask=0x80000000, lower_mask=0x7FFFFFFF, a=0x9908B0DF, m=397):
        '''
            This method models MT19937 function as a Z3 program
        '''
        MT = [i for i in MT] #Just a shallow copy of the state

        for i in range(n):
            x = (MT[i] & upper_mask) + (MT[(i+1) % n] & lower_mask)
            xA = LShR(x, 1)
            xB = If(x & 1 == 0, xA, xA ^ a) #Possible Z3 optimization here by declaring auxiliary symbolic variables
            MT[i] = MT[(i + m) % n] ^ xB

        return MT

    def get_symbolic(self, guess):
        name = next(SYMBOLIC_COUNTER)
        ERROR = 'Must pass a string like "?1100???1001000??0?100?10??10010" where ? represents an unknown bit'

        assert type(guess) == str, ERROR
        assert all(map(lambda x: x in '01?', guess)), ERROR
        assert len(guess) <= 32, "One 32-bit number at a time please"
        guess = guess.zfill(32)

        self.symbolic_guess = BitVec(f'symbolic_guess_{name}', 32)
        guess = guess[::-1]

        for i, bit in enumerate(guess):
            if bit != '?':
                self.solver.add(Extract(i, i, self.symbolic_guess) == bit)

        return self.symbolic_guess


    def submit(self, guess):
        '''
            You need 624 numbers to completely clone the state.
                You can input less than that though and this will give you the best guess for the state
        '''
        if self.index >= 624:
            name = next(SYMBOLIC_COUNTER)
            next_mt = self.symbolic_twist(self.MT)
            self.MT = [BitVec(f'MT_{i}_{name}', 32) for i in range(624)]
            for i in range(624):
                self.solver.add(self.MT[i] == next_mt[i])
            self.index = 0

        symbolic_guess = self.get_symbolic(guess)
        symbolic_guess = self.symbolic_untamper(self.solver, symbolic_guess)
        self.solver.add(self.MT[self.index] == symbolic_guess)
        self.index += 1

    def get_random(self):
        '''
            This will give you a random.Random() instance with the cloned state.
        '''
        logger.debug('Solving...')
        start = time.time()
        print(self.solver.check())
        model = self.solver.model()
        end = time.time()
        logger.debug(f'Solved! (in {round(end-start,3)}s)')

        #Compute best guess for state
        state = list(map(lambda x: model[x].as_long(), self.MT))
        result_state = (3, tuple(state+[self.index]), None)
        r = Random()
        r.setstate(result_state)
        return r

#below code, the actual exploit, is mine
import gmpy2
from pwn import *

ut = Untwister()
sh = remote('crypto.zh3r0.cf', 4444)
for ii in range(624):
    print(ii)
    sh.recvline()
    sh.sendline(b'0')
    lin = sh.recvline()
    flag = False
    sc = lin.decode().strip().split('round score: ')[1]
    if '/' in sc:
        score = sc.split('/')
    else:
        score = sc
        flag = True
    if not flag:
        numer = int(score[0])
        denom = int(score[1])
        state_comb = gmpy2.c_div(gmpy2.mpz(9007199254740992) * gmpy2.mpz(denom), numer) + 1 # solve for state
        bits = bin(state_comb)[2:]
        bits = '0' * (53 - len(bits)) + bits
        a = bits[:27] #upper
        b = bits[27:] #lower
        assert len(a) == 27
        assert len(b) == 26
        ut.submit(a + '?' * 5) #a is truncated 5 bits
        ut.submit(b[:13] + '?' * 19) # b bits are imprecise, take only 13
    else:
        ut.submit('0' * 10 + '?' * 22) #we only know that the first 10 bits are 0 (1/1024)
        ut.submit('?' * 16 + '?' * 16)

rec = ut.get_random()

#score 1024!
while True:
    print(sh.recvline())
    sh.sendline(str(rec.random()))
    print(sh.recvline())