2022wmctf

WMCTF2022

解题情况

Crypto

nanoDiamond

题目

from Crypto.Util.number import *
import string
import secrets
from hashlib import sha256
from random import randint, shuffle, choice

def proof_of_work():
    s = ''.join([secrets.choice(string.digits + string.ascii_letters)
                for _ in range(20)])
    print(f'sha256(XXXX+{s[4:]}) == {sha256(s.encode()).hexdigest()}')
    if input('Give me XXXX: ') != s[:4]:
        exit(1)

ROUND_NUM = 50
PREROUND_NUM = 14
CHEST_NUM = 6

flag = b'flag{test}'

white_list = ['==','(',')','0','1','and','or','B0','B1','B2','B3','B4','B5']

def calc(ans, chests, expr):
    B0, B1, B2, B3, B4, B5 = chests
    return ans(eval(expr))

def round():
    chests = [choice((True, False)) for _ in range(CHEST_NUM)]
    print("Six chests lie here, with mimics or treasure hidden inside.")
    print("But don't worry. Skeleton Merchant knows what to do.")
    print("Be careful, Skeleton Merchant can lie twice!")

    truth = lambda r: not not r
    lie = lambda r: not r
    lie_num = randint(0, 2)
    lie_status = [truth] * (PREROUND_NUM - lie_num) + [lie] * lie_num
    shuffle(lie_status)

    for i in range(PREROUND_NUM):
        try:
            question = input('Question: ').strip()
            for word in question.split(' '):
                print(word)
                assert word in white_list, f"({word}) No treasure for dirty hacker!"
            result = calc(lie_status[i], chests, question)
            print(f'Answer: {result}!')
        except Exception as e:
            print("Skeleton Merchant fails to understand your words.")
            print(e)
    print('Now open the chests:')
    return chests == list(map(int, input().strip().split(' ')))


if __name__ == '__main__':

    proof_of_work()

    print('Terraria is a land of adventure! A land of mystery!')
    print('Can you get all the treasure without losing your head?')

    for i in range(ROUND_NUM):
        if not round():
            print('A chest suddenly comes alive and BITE YOUR HEAD OFF.')
            exit(0)
        else:
            print('You take all the treasure safe and sound. Head to the next vault!')

    print(f"You've found all the treasure! {flag}")

题解

starctf2022同类型题，信息论中利用生成多项式与循环码纠正错误

找到wp，原题是（15，7），这里是（14，6），因此生成多项式不用改动，改参数即可

part1

# from pwn import *

# context.log_level = 'debug'

R.<x>= PolynomialRing(GF(2))
g = x ^ 8 + x ^ 7 + x ^ 6 + x ^ 4 + 1


def n2p(a):
    a = bin(a)[2:]
    p = 0
    for i in range(len(a)):
        if a[len(a) - i - 1] == '1':
            p += x ^ i
    return p


def enc(i):
    m = n2p(i)
    c = (x ^ 8) * m + (((x ^ 8) * m) % g)
    return "".join([str(int(i in c.exponents())) for i in range(14)])[::-1]


dic = []
for i in range(2 ** 6):
    dic.append(enc(i))

part = "( B0 == {} and B1 == {} and B2 == {} and B3 == {} and B4 == {} and B5 == {}) "
questions = []
for i in range(14):
    question = ""
    nums = [j[:6] for j in dic if j[i] == '1']
    assert (len(nums) == 32)
    for j in range(32):
        n = nums[j]
        question += part.format(n[0], n[1], n[2], n[3], n[4], n[5]) + "or "
    questions.append(question[:-4])  # ?


def dif(a, b):
    cnt = 0
    for i in range(len(a)):
        if a[i] != b[i]:
            cnt += 1
    return cnt

print(questions)
print(dic)

part2

from pwn import *
import hashlib
from string import ascii_letters, digits
from itertools import product


def dif(a, b):
    cnt = 0
    for i in range(len(a)):
        if a[i] != b[i]:
            cnt += 1
    return cnt


table = ascii_letters + digits

context.log_level = 'debug'
questions = [
    '( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)',
    '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)']
questions = [i.replace(')', ' )') for i in questions]
dic = ['00000000000000', '00000111010001', '00001001110011', '00001110100010', '00010011100110', '00010100110111',
       '00011010010101', '00011101000100', '00100000011101', '00100111001100', '00101001101110', '00101110111111',
       '00110011111011', '00110100101010', '00111010001000', '00111101011001', '01000000111010', '01000111101011',
       '01001001001001', '01001110011000', '01010011011100', '01010100001101', '01011010101111', '01011101111110',
       '01100000100111', '01100111110110', '01101001010100', '01101110000101', '01110011000001', '01110100010000',
       '01111010110010', '01111101100011', '10000001110100', '10000110100101', '10001000000111', '10001111010110',
       '10010010010010', '10010101000011', '10011011100001', '10011100110000', '10100001101001', '10100110111000',
       '10101000011010', '10101111001011', '10110010001111', '10110101011110', '10111011111100', '10111100101101',
       '11000001001110', '11000110011111', '11001000111101', '11001111101100', '11010010101000', '11010101111001',
       '11011011011011', '11011100001010', '11100001010011', '11100110000010', '11101000100000', '11101111110001',
       '11110010110101', '11110101100100', '11111011000110', '11111100010111']
# 1.13.154.182:30310
r = remote('1.13.154.182', 30310)

# proof of work
proof = r.recvuntil(b'Give me XXXX: ')
print(proof)
tail = proof[12:28].decode()
_hash = proof[33:97].decode()
print(tail)
print(_hash)
print('开始爆破！')
for i in product(table, repeat=4):
    head = ''.join(i)
    t = hashlib.sha256((head + tail).encode()).hexdigest()
    if t == _hash:
        r.sendline(head.encode())
        print('爆破成功！结果是：', end='')
        print(head)
        break

for i in range(50):
    msg = ''
    for j in range(14):
        # r.recvuntil("Question: ")
        # r.send(questions[j])
        r.sendlineafter("Question: ", questions[j])
        r.recvuntil("Answer: ")
        if b'True' in r.recvuntil("!"):
            msg += '1'
        else:
            msg += '0'
    for j in range(64):  # 32*2 = 64
        if (dif(msg, dic[j]) <= 2):
            break
    ans = ""
    for k in dic[j][:6]:
        ans += k + " "
    r.sendlineafter("chests:", ans)
r.interactive()
# You take all the treasure safe and sound. Head to the next vault!
# You've found all the treasure! WMCTF{TERR4R1a_IS_4_LAND_0F_@DVENturE}

WMCTF{TERR4R1a_IS_4_LAND_0F_@DVENturE}

nanoDiamond - rev

题目

# from Crypto.Util.number import *
import string
import secrets
from hashlib import sha256
from random import randint, shuffle, choice

def proof_of_work():
    s = ''.join([secrets.choice(string.digits + string.ascii_letters)
                for _ in range(20)])
    print(f'sha256(XXXX+{s[4:]}) == {sha256(s.encode()).hexdigest()}')
    if input('Give me XXXX: ') != s[:4]:
        exit(1)

ROUND_NUM = 50
PREROUND_NUM = 13
CHEST_NUM = 6

with open('flag', 'r') as f:
    flag = f.read()

white_list = ['==','(',')','0','1','and','or','B0','B1','B2','B3','B4','B5']

def calc(ans, chests, expr):
    B0, B1, B2, B3, B4, B5 = chests
    return ans(eval(expr))

def round():
    chests = [choice((True, False)) for _ in range(CHEST_NUM)]
    print("Six chests lie here, with mimics or treasure hidden inside.")
    print("But don't worry. Skeleton Merchant knows what to do.")
    print("Be careful, Skeleton Merchant can lie twice!")

    truth = lambda r: not not r
    lie = lambda r: not r
    lie_num = randint(0, 2)
    lie_status = [truth] * (PREROUND_NUM - lie_num) + [lie] * lie_num
    shuffle(lie_status)

    for i in range(PREROUND_NUM):
        try:
            question = input('Question: ').strip()
            for word in question.split(' '):
                assert word in white_list, f"({word}) No treasure for dirty hacker!"
            result = calc(lie_status[i], chests, question)
            print(f'Answer: {result}!')
        except Exception as e:
            print("Skeleton Merchant fails to understand your words.")
            print(e)
    print('Now open the chests:')
    return chests == list(map(int, input().strip().split(' ')))


if __name__ == '__main__':

    proof_of_work()

    print('Terraria is a land of adventure! A land of mystery!')
    print('Can you get all the treasure without losing your head?')

    for i in range(ROUND_NUM):
        if not round():
            print('A chest suddenly comes alive and BITE YOUR HEAD OFF.')
            exit(0)
        else:
            print('You take all the treasure safe and sound. Head to the next vault!')

    print(f"You've found all the treasure! {flag}")

题解

简单入门循环码生成多项式等概念与性质

题中n=13，k=6，而$x ^{13} - 1$或$x ^ { 13 } + 1$因式分解组合不出7（13-6）次多项式

随便找了个(15, 8)的生成多项式，无脑爆破

运气好，出了

part1

# from pwn import *

# context.log_level = 'debug'

R.<x>= PolynomialRing(GF(2))
g = x^7+x^6+x^4+1


def n2p(a):
    a = bin(a)[2:]
    p = 0
    for i in range(len(a)):
        if a[len(a) - i - 1] == '1':
            p += x ^ i
    return p


def enc(i):
    m = n2p(i)
    c = (x ^ 7) * m + (((x ^ 7) * m) % g)
    return "".join([str(int(i in c.exponents())) for i in range(13)])[::-1]


dic = []
for i in range(2 ** 6):
    dic.append(enc(i))

part = "( B0 == {} and B1 == {} and B2 == {} and B3 == {} and B4 == {} and B5 == {}) "
questions = []
for i in range(13):
    question = ""
    nums = [j[:6] for j in dic if j[i] == '1']
    print(len(nums))
    assert (len(nums) == 32)
    for j in range(32):
        n = nums[j]
        question += part.format(n[0], n[1], n[2], n[3], n[4], n[5]) + "or "
    questions.append(question[:-4])  # ?


def dif(a, b):
    cnt = 0
    for i in range(len(a)):
        if a[i] != b[i]:
            cnt += 1
    return cnt

print(questions)
print(dic)

part2

from pwn import *
import hashlib
from string import ascii_letters, digits
from itertools import product


def dif(a, b):
    cnt = 0
    for i in range(len(a)):
        if a[i] != b[i]:
            cnt += 1
    return cnt



table = ascii_letters + digits

context.log_level = 'debug'
questions = ['( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0)', '( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1)', '( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 0 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 0 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 0 and B3 == 1 and B4 == 1 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 0 and B5 == 0) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 0 and B4 == 1 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 0 and B5 == 1) or ( B0 == 1 and B1 == 1 and B2 == 1 and B3 == 1 and B4 == 1 and B5 == 0)']
questions = [i.replace(')', ' )') for i in questions]
dic = ['0000000000000', '0000011010001', '0000101110011', '0000110100010', '0001000110111', '0001011100110', '0001101000100', '0001110010101', '0010001101110', '0010010111111', '0010100011101', '0010111001100', '0011001011001', '0011010001000', '0011100101010', '0011111111011', '0100000001101', '0100011011100', '0100101111110', '0100110101111', '0101000111010', '0101011101011', '0101101001001', '0101110011000', '0110001100011', '0110010110010', '0110100010000', '0110111000001', '0111001010100', '0111010000101', '0111100100111', '0111111110110', '1000000011010', '1000011001011', '1000101101001', '1000110111000', '1001000101101', '1001011111100', '1001101011110', '1001110001111', '1010001110100', '1010010100101', '1010100000111', '1010111010110', '1011001000011', '1011010010010', '1011100110000', '1011111100001', '1100000010111', '1100011000110', '1100101100100', '1100110110101', '1101000100000', '1101011110001', '1101101010011', '1101110000010', '1110001111001', '1110010101000', '1110100001010', '1110111011011', '1111001001110', '1111010011111', '1111100111101', '1111111101100']
# 1.13.154.182:31888
while True:
    try:
        r = remote('1.13.154.182', 31888)

        # proof of work
        proof = r.recvuntil(b'Give me XXXX: ')
        print(proof)
        tail = proof[12:28].decode()
        _hash = proof[33:97].decode()
        print(tail)
        print(_hash)
        print('开始爆破！')
        for i in product(table, repeat=4):
            head = ''.join(i)
            t = hashlib.sha256((head + tail).encode()).hexdigest()
            if t == _hash:
                r.sendline(head.encode())
                print('爆破成功！结果是：', end='')
                print(head)
                break

        for i in range(50):
            msg = ''
            for j in range(13):
                # r.recvuntil("Question: ")
                # r.send(questions[j])
                r.sendlineafter("Question: ", questions[j])
                r.recvuntil("Answer: ")
                if b'True' in r.recvuntil("!"):
                    msg += '1'
                else:
                    msg += '0'
            for j in range(64):  # 32*2 = 64
                if (dif(msg, dic[j]) <= 2):
                    break
            ans = ""
            for k in dic[j][:6]:
                ans += k + " "
            r.sendlineafter("chests:", ans)
        r.interactive()
    except:
        continue
    break
# WMCTF{7ErrAr14_Is_a_lAND_0F_AdVeNTURe!!!!!}

WMCTF{7ErrAr14_Is_a_lAND_0F_AdVeNTURe!!!!!}

ecc

题目

flag bits: 606
e = 0x10001
n = 61262574892917665379101848600282751252633178779864648655116434051615964747592676204833262666589440081296571836666022795166255640192795587508845265816642144669301520989571990670507103278098950563219296310830719975959589061794360407053224254135937766317251283933110936269282950512402428088733821277056712795259
c = 16002162436420434728223131316901476099110904029045408221515087977802746863468505266500673611412375885221860212238712311981079623398373906773247773552766200431323537510699147642358473715224124662007742017000810447999989426207919068340364725395075614636875116086496704959130761547095168937180751237132642548997
G = (3364552845709696244757995625685399274809023621531082895612949981433844727622567352338990765970534554565693355095508508160162961299445890209860508127449468 : 4874111773041360858453223185020051270111929505293131058858547656851279111764112235653823943997681930204977283843433850957234770591933663960666437259499093 : 1)
3G = (8240596254289477251157504980772167439041663401504657696787046343848644902166655624353107697436635678388969190302189718026343959470011854412337179727187240 : 4413479999185843948404442728411950785256136111461847698098967018173326770728464491960875264034301169184074110521039566669441716138955932362724194843596479 : 1)

hint：wmctf{a+b+c}

题解

factordb分解出n，根据提示将a、b、m二进制补位并拼接

import libnum,gmpy2
# flag bits: 606
e = 0x10001
n = 61262574892917665379101848600282751252633178779864648655116434051615964747592676204833262666589440081296571836666022795166255640192795587508845265816642144669301520989571990670507103278098950563219296310830719975959589061794360407053224254135937766317251283933110936269282950512402428088733821277056712795259
c = 16002162436420434728223131316901476099110904029045408221515087977802746863468505266500673611412375885221860212238712311981079623398373906773247773552766200431323537510699147642358473715224124662007742017000810447999989426207919068340364725395075614636875116086496704959130761547095168937180751237132642548997
x1, y1 = (3364552845709696244757995625685399274809023621531082895612949981433844727622567352338990765970534554565693355095508508160162961299445890209860508127449468 , 4874111773041360858453223185020051270111929505293131058858547656851279111764112235653823943997681930204977283843433850957234770591933663960666437259499093)
x3, y3 = (8240596254289477251157504980772167439041663401504657696787046343848644902166655624353107697436635678388969190302189718026343959470011854412337179727187240 , 4413479999185843948404442728411950785256136111461847698098967018173326770728464491960875264034301169184074110521039566669441716138955932362724194843596479)
tmp1 = x1^3-y1^2
tmp2 = x3^3-y3^2
tmp = (tmp2-tmp1)
p = 8308060309959524788634404677678479024666400240233812713350984932475838872076486898595574202532027412806488106365658717017155800093596205985127436125626827

# tmp = x3^3-x1^3-y3^2+y1^2  # tmp = a(x1-x3)+kp
# R.<a> = PolynomialRing(Zmod(p))
# f = a*(x1-x3)-tmp
# print(f.roots())

a = 3629864911627283784723617758993690217446918991113173559686999
print((tmp-a*(x1-x3))%p)  # 验证a
b = (y3^2-x3^3-a*x3)%p
q = n//p
d = int(gmpy2.invert(e, (p-1)*(q-1)))
flag = int(pow(c,d,n))
print(libnum.n2s(int(pow(c,d,n))))

####
print('a', int(a).bit_length())
print('b', int(b).bit_length())
print('flag',int(flag).bit_length())
print('p =',p)
print('a =', a)
print('b =', b)
tmp = str(a)+str(b)+str(flag)
# tmp = a+b+flag
def pad(num):
    print(len('0'*(202-len(str(bin(num)[2:])))+str(bin(num)[2:])))
    return('0'*(202-len(str(bin(num)[2:])))+str(bin(num)[2:]))
flag = int(pad(a)+pad(b)+pad(flag),2)
print(libnum.n2s(flag))
# b'$$U_c0u1d_s01v3_e11iptiCurv3_s0_34sily$$0f19d82199a0db0dee31fa12330307ea90aa'

wmctf{$$U_c0u1d_s01v3_e11iptiCurv3_s0_34sily$$0f19d82199a0db0dee31fa12330307ea90aa}

homo

题目

• gentry.py

  from Crypto.Util.number import *
  from secret import flag
  from random import *
  
  assert flag.startswith(b'wmctf{') and flag.endswith(b'}')
  flaglen = len(flag) - 7
  flag = bytes_to_long(flag[6:-1])
  pbit = 114
  qbit = 514
  rbit = 191
  keylen = 981
  nouse = 0
  
  
  def keygen():
      pk = []
      sk = getPrime(qbit)
      for i in range(keylen):
          print(i)
          p = getPrime(pbit)
          r = getPrime(rbit)
          pk.append(p * sk + 2 * r)
      return pk, sk
  
  
  def enc(m, pk):
      c = []
      m = [int(i) for i in bin(m)[2:]]  # 转二进制
      print(m)
      for i in m:
          tempc = i
          for j in range(keylen):
              if randint(0, 1):
                  tempc += pk[j]
          c.append(tempc)
      return c
  
  
  pk, sk = keygen()
  print(sk)
  c = enc(flag, pk)
  
  f = open('./pubkey.txt', 'w')
  f.write(str(pk))
  f.close()
  
  f = open('./cipher.txt', 'w')
  f.write(str(c))
  f.close()
  print([(i % sk) % 2 for i in c])
  print(sk)

• pubkey.txt

• cipher.txt

题解

搜索思路

• https://tover.xyz/p/wieners-lattices-equations/#What-about-a-iX-equiv-y-i-pmod-P-i-s-i -> 21wmctf lsb

• https://hackmd.io/@crazyman/BJXeu3abY#Easylsb -> https://martinralbrecht.wordpress.com/2020/03/21/the-approximate-gcd-problem/ -> AGCD

相关参考

• AGCD SDA attack code https://github.com/mathno1/Lattice/tree/main/AGCD

• Paper https://eprint.iacr.org/2016/215.pdf

  

f = open('/Users/0HB/Desktop/复现/wm/homo/pubkey.txt', 'r')
pk_ = f.read()
x = []
eval('x.extend({})'.format(pk_))
f.close()

f = open('/Users/0HB/Desktop/复现/wm/homo/cipher.txt', 'r')
c_ = f.read()
ct = []
eval('ct.extend({})'.format(c_))
f.close()

def SDA(x, t, gamma, rho, eta):
    M = Matrix(ZZ, t, t)
    M[0, 0] = 2^(rho+1)
    for i in range(1, t):
        M[0, i] = x[i]
        M[i, i] = -x[0]
        
    print('Matirx done')
    ML = M.LLL()
    print('LLL done!')
#     f = open('/Users/0HB/Desktop/复现/wm/homo/LLL.txt', 'w')
#     f.write(str(ML))
#     f.close()
#     print('Save LLL')

    d = ML.determinant()
#     assert d == 2^(rho + 1) * x[0]^(t - 1)
#     assert sqrt(t)*2^(gamma - eta + rho + 1) < sqrt(t/(2*pi*e))*d^(1/t)

    v = ML[0]
    min = abs(norm(ML[0]) - sqrt(t)*2^(gamma - eta + rho + 1))
    for i in ML:
        if min > abs(norm(i) - sqrt(t)*2^(gamma - eta + rho + 1)):
            min = abs(norm(i) - sqrt(t)*2^(gamma - eta + rho + 1))
            v = i

    # v[0] = 2^(rho + 1) * q_0
    q0 = v[0] // 2^(rho + 1)
    r0 = x[0] % q0
    print(q0)
    print('p =', q0)
    print('r =', r0)
    p = (x[0] - r0) // q0
    print("sk:{}".format(p))

    return p


def decryption(ct, p):
    ct = '0b' + ''.join(str(i%p%2) for i in ct)
    m = int(ct, 2).to_bytes((len(ct) - 1) // 8, byteorder='big').decode()
    return m

if __name__ == "__main__":
    t = 981
    gamma = 628  # 514+114
    eta = 514
    rho = 191
    p = SDA(x, t, gamma, rho, eta)
    print(decryption(ct, p))

output

Matirx done
LLL done!
17195743943555229331660961462727499
p = 17195743943555229331660961462727499
r = 2615830010834467677351383140406463
sk:41565572874253689464437825525802665878958533473562648432875965578230785556539072257838190060392315994424904212374664222250474284551897781086850148587327684

r>p，所以上面求得的r、sk是不准的，可以利用整除p平方（p平方大于2r）的思想消除r影响，求得真正的私钥sk

get flag

import sys

import libnum, gmpy2
from Crypto.Util.number import *
from random import *

f = open('/Users/0HB/Desktop/复现/wm/homo/pubkey.txt', 'r')
pk_ = f.read()
pks = []
eval('pks.extend({})'.format(pk_))
f.close()

f = open('/Users/0HB/Desktop/复现/wm/homo/cipher.txt', 'r')
c_ = f.read()
cs = []
eval('cs.extend({})'.format(c_))
f.close()

"""
# c = p*sk+2*r
c = 714750948012851406500586517157106717606895617539492838332982483584450804764237803294239970247209996859617533175677756145984683775979560835419919499626250456011382074927666818288229451188779
p = 17195743943555229331660961462727499

# 不准
r = 2615830010834467677351383140406463 # 2*r % p
sk:41565572874253689464437825525802665878958533473562648432875965578230785556539072257838190060392315994424904212374664222250474284551897781086850148587327684
"""

def decryption(ct, p):
    ct = '0b' + ''.join(str(i % p % 2) for i in ct)
    m = int(ct, 2).to_bytes((len(ct) - 1) // 8, byteorder='big')
    return m


# x = p*sk+2*r
x = pks[0]
p = 17195743943555229331660961462727499
r = 2615830010834467677351383140406463
sk0 = 41565572874253689464437825525802665878958533473562648432875965578230785556539072257838190060392315994424904212374664222250474284551897781086850148587327684
print(decryption(cs, sk0))
sk = ((x//(p**2))*(p**2))//p
print(decryption(cs, sk))
# b'sodayo>A<!!$%!$_Easy_G@CDp_ATtaCk'

wmctf{sodayo>A<!!$%!$_Easy_G@CDp_ATtaCk}

INTERCEPT

人菜+时间不够了

OCOCOCB

2021年

• https://hackmd.io/@crazyman/BJXeu3abY#baby_ocb
• https://zhuanlan.zhihu.com/p/405493136

简单看了下往年wp，没思路就没看了