uiu-hastad-solve.py

import sys
import binascii
from Crypto.PublicKey import RSA
from base64 import b64decode
import itertools

e = 3
# a = ["10652cdfaa86ddbee1409ac7ac327a0c848081ee6e3b110867085f1074755785b0a5a6a2343b791695c3e91fdb370d5b26be3b6d2fc449c7788bbb1ab67ddc361b4115010618e39c883449b757fc1624369b440236ee65", "10652cdfaa8c9ef24fc044b5fed749888632ad132bd412f22d9d905e6ffd27b288c22884b24fe130d83aaab9c2dc6e942418dff89d2b66a66e40900db9456813d70eb63d0c38697f89ff387969d3d40163376416270965", "10652cdfaa8ab16290cf92bacf31b23d6a0ea95c2ebd6eb8afe4f038d852a7f17e98f965f299b4d00126611d403c5208a145157ed1d71079fc558eaa888e993360fac35c7a816ad183190867b1b7580a2677cd6871aa65", "10652cdfaa86ddbee1409ac7ac327a0c848081ee6e3b110867085f1074755785b0a5a6a2343b791695c3e91fdb370d5b26be3b6d2fc449c7788bbb1ab67ddc361b4115010618e39c883449b757fc1624369b440236ee65", "10652cdfaa875a9ac01e472ea5896c1d460410508b9a7c723b5ba904fb5b64d68a1e96254ba04b08c92d51f1fe6c3d6bb426e1ee8c61c8a6ff1eeab9e07f51d8057f2f0c54b27c7006539f7148484ff26a02e4cb1d3165", "10652cdfaa8c9ef24fc044b5fed749888632ad132bd412f22d9d905e6ffd27b288c22884b24fe130d83aaab9c2dc6e942418dff89d2b66a66e40900db9456813d70eb63d0c38697f89ff387969d3d40163376416270965", "10652cdfaa875a9ac01e472ea5896c1d460410508b9a7c723b5ba904fb5b64d68a1e96254ba04b08c92d51f1fe6c3d6bb426e1ee8c61c8a6ff1eeab9e07f51d8057f2f0c54b27c7006539f7148484ff26a02e4cb1d3165", "10652cdfaa8210601d22f4a15aa380233420f9ee9a276d3ac8e05cfc4f6f515f78331e8e74484e8533221e88f78671dd08622e78233e458978a35036680d1c5caaba2fa3bce3b914ad48501a276d6a88adc16db282e065", "10652cdfaa8ab16290cf92bacf31b23d6a0ea95c2ebd6eb8afe4f038d852a7f17e98f965f299b4d00126611d403c5208a145157ed1d71079fc558eaa888e993360fac35c7a816ad183190867b1b7580a2677cd6871aa65", "10652cdfaa8c2701b8bb7c11fc3218cc2d97cd4707f6de55637bc093f474d231b4d4fe8635261b8e4f772d0e51a25f8e713777a137be6f04e0d28ddd6ec0b852aaf357d33e08aed23e034fcd1ced38542fbeb5aa0eee65", "10652cdfaa8210601d22f4a15aa380233420f9ee9a276d3ac8e05cfc4f6f515f78331e8e74484e8533221e88f78671dd08622e78233e458978a35036680d1c5caaba2fa3bce3b914ad48501a276d6a88adc16db282e065", "10652cdfaa8c9ef24fc044b5fed749888632ad132bd412f22d9d905e6ffd27b288c22884b24fe130d83aaab9c2dc6e942418dff89d2b66a66e40900db9456813d70eb63d0c38697f89ff387969d3d40163376416270965", "10652cdfaa8ab162128a955a58d3b780f2656800796eb70c345c56d7b8523d614ef4ca920471f56493c83ca48500033a0c0b31988ca6e66a76e0ed559b38616688941558b127260cdf70261822929efa0aa6b6d79d1665", "10652cdfaa8ab162128a955a58d3b780f2656800796eb70c345c56d7b8523d614ef4ca920471f56493c83ca48500033a0c0b31988ca6e66a76e0ed559b38616688941558b127260cdf70261822929efa0aa6b6d79d1665", "10652cdfaa8c2701b8bb7c11fc3218cc2d97cd4707f6de55637bc093f474d231b4d4fe8635261b8e4f772d0e51a25f8e713777a137be6f04e0d28ddd6ec0b852aaf357d33e08aed23e034fcd1ced38542fbeb5aa0eee65"]
a = [0x10652cdfaa86ddbee1409ac7ac327a0c848081ee6e3b110867085f1074755785b0a5a6a2343b791695c3e91fdb370d5b26be3b6d2fc449c7788bbb1ab67ddc361b4115010618e39c883449b757fc1624369b440236ee65, 0x10652cdfaa8c9ef24fc044b5fed749888632ad132bd412f22d9d905e6ffd27b288c22884b24fe130d83aaab9c2dc6e942418dff89d2b66a66e40900db9456813d70eb63d0c38697f89ff387969d3d40163376416270965, 0x10652cdfaa8ab16290cf92bacf31b23d6a0ea95c2ebd6eb8afe4f038d852a7f17e98f965f299b4d00126611d403c5208a145157ed1d71079fc558eaa888e993360fac35c7a816ad183190867b1b7580a2677cd6871aa65, 0x10652cdfaa86ddbee1409ac7ac327a0c848081ee6e3b110867085f1074755785b0a5a6a2343b791695c3e91fdb370d5b26be3b6d2fc449c7788bbb1ab67ddc361b4115010618e39c883449b757fc1624369b440236ee65, 0x10652cdfaa875a9ac01e472ea5896c1d460410508b9a7c723b5ba904fb5b64d68a1e96254ba04b08c92d51f1fe6c3d6bb426e1ee8c61c8a6ff1eeab9e07f51d8057f2f0c54b27c7006539f7148484ff26a02e4cb1d3165, 0x10652cdfaa8c9ef24fc044b5fed749888632ad132bd412f22d9d905e6ffd27b288c22884b24fe130d83aaab9c2dc6e942418dff89d2b66a66e40900db9456813d70eb63d0c38697f89ff387969d3d40163376416270965, 0x10652cdfaa875a9ac01e472ea5896c1d460410508b9a7c723b5ba904fb5b64d68a1e96254ba04b08c92d51f1fe6c3d6bb426e1ee8c61c8a6ff1eeab9e07f51d8057f2f0c54b27c7006539f7148484ff26a02e4cb1d3165, 0x10652cdfaa8210601d22f4a15aa380233420f9ee9a276d3ac8e05cfc4f6f515f78331e8e74484e8533221e88f78671dd08622e78233e458978a35036680d1c5caaba2fa3bce3b914ad48501a276d6a88adc16db282e065, 0x10652cdfaa8ab16290cf92bacf31b23d6a0ea95c2ebd6eb8afe4f038d852a7f17e98f965f299b4d00126611d403c5208a145157ed1d71079fc558eaa888e993360fac35c7a816ad183190867b1b7580a2677cd6871aa65, 0x10652cdfaa8c2701b8bb7c11fc3218cc2d97cd4707f6de55637bc093f474d231b4d4fe8635261b8e4f772d0e51a25f8e713777a137be6f04e0d28ddd6ec0b852aaf357d33e08aed23e034fcd1ced38542fbeb5aa0eee65, 0x10652cdfaa8210601d22f4a15aa380233420f9ee9a276d3ac8e05cfc4f6f515f78331e8e74484e8533221e88f78671dd08622e78233e458978a35036680d1c5caaba2fa3bce3b914ad48501a276d6a88adc16db282e065, 0x10652cdfaa8c9ef24fc044b5fed749888632ad132bd412f22d9d905e6ffd27b288c22884b24fe130d83aaab9c2dc6e942418dff89d2b66a66e40900db9456813d70eb63d0c38697f89ff387969d3d40163376416270965, 0x10652cdfaa8ab162128a955a58d3b780f2656800796eb70c345c56d7b8523d614ef4ca920471f56493c83ca48500033a0c0b31988ca6e66a76e0ed559b38616688941558b127260cdf70261822929efa0aa6b6d79d1665, 0x10652cdfaa8ab162128a955a58d3b780f2656800796eb70c345c56d7b8523d614ef4ca920471f56493c83ca48500033a0c0b31988ca6e66a76e0ed559b38616688941558b127260cdf70261822929efa0aa6b6d79d1665, 0x10652cdfaa8c2701b8bb7c11fc3218cc2d97cd4707f6de55637bc093f474d231b4d4fe8635261b8e4f772d0e51a25f8e713777a137be6f04e0d28ddd6ec0b852aaf357d33e08aed23e034fcd1ced38542fbeb5aa0eee65]
n = [0xbc4ec2b74d85fb57ec07f538b59987c1150042ef76178b7af6dc09ca139dc8570226fe0317f3b73e8f98de38eb03a986496431d8526be4e65d47d86130a4370348b8a8dbba80d922f4dbac31b95f1028baac1ba8f8cab00d6e362c761da0dece81a700b92a5c1d79ec50451b3147805123e92f424d422d688ab020280d35384f, 0xd83a59170679b7d8b2199e98656717c515e06e44e65b5f7b687e4fec6d21a7e6e75ecbcf208202f210ef8e29a7ad44ab72914b1f35d502f6d7f657e5512d4b989773515cbc046ca3ffef37f3090548ac1086d96c96fe7edb9bdeb58ba635fa1582da4a85357105293139c8152d70c2ec5ec667bb91197c353cd6aafac73476df, 0xc39ab84fbf6709048427c05dbd303f0ba2f90ecdd51a809f1d8da9df0546a771e982a6bccb299c4bf12d1b0b11df88b0627563d726bb70c5121cb5722c75e35b54e6d43d09443738fe3ac8e5a8bb74b1667ddf6592359d9fc65a05a32b98a50c52f1339ed8b5fab5616d52d81a11579a83fc33e069c4d9cfb93b24d752937ced]

def chinese_remainder(n, a):
    sum = 0
    prod = reduce(lambda a, b: a*b, n)
 
    for n_i, a_i in zip(n, a):
        p = prod / n_i
        sum += a_i * mul_inv(p, n_i) * p
    return sum % prod
 
 
def mul_inv(a, b):
    b0 = b
    x0, x1 = 0, 1
    if b == 1: return 1
    while a > 1:
        q = a / b
        a, b = b, a%b
        x0, x1 = x1 - q * x0, x0
    if x1 < 0: x1 += b0
    return x1

def find_invpow(x,n):
    high = 1
    while high ** n < x:
        high *= 2
    low = high/2
    while low < high:
        mid = (low + high) // 2
        if low < mid and mid**n < x:
            low = mid
        elif high > mid and mid**n > x:
            high = mid
        else:
            return mid
    return mid + 1

if __name__ == '__main__':
    # [a[0].decode("hex"),a[1].decode("hex"),a[2].decode("hex")]
    for x_a in itertools.permutations(a,3):
      result = (chinese_remainder(n, x_a))
      resultHex = str(hex(find_invpow(result,3)))[2:-1]
      if len(resultHex) % 2 == 1:
        resultHex = "0" + resultHex
      if "flag" in resultHex.decode("hex"):
        print resultHex.decode("hex")
        sys.exit(0)