2020BJDasa

可以发现两个n公用了一个p,那么求取两个n的最大公因数就可以得到p,这样一来两个n就都可以被分解了。

import gmpy2 as gp
from Crypto.Util.number import long_to_bytes
n1=0x661d752110bcc6ee5ca33edaf244716cccce6400dfdbfd84ce6ae2d8fbbeb2f61584da7668768403b6135e7810eae9d4d8e044935f8680de5324c3fc0f9bffb01812f9d2ac9055ee8dbd17b90c5a60cb7595a82f24a075d951db3b7f913b8543ecd52b8c8464ce348c3970d511ae911e814f9ca33b8412db2730e61820f5de47
p=9540203717217880059997385799331301649727503984010337568404427747385824530958536656147747848448822264268428226235860927158082497191830274046098671199542207
c1=0xd7931796fa39cfa37c0b621c01175904206dff1d74a28369dcd6517957ed76c5eb7d4934cbeb902119f9215f9ae7926debe3abe856244b45dbb4caaa2b93dbb79a3ca1a9813e1466c49fe3c03e5462811afbf3f40ff79927f9fe3681b7f3cef34466b9a736512f4931b5026eefacbae9be6e408085a7a636c514574c3b22ffe
q=n1//p
phi=(p-1)*(q-1)
e=65537
d=gp.invert(e,phi)
m=pow(c1,d,n1)
print(long_to_bytes(m))
#key=b'\x89)\xef\x12\xa1\x7f\x14[\xc9\xb4\x8a\xfa,\x88\xa2\xef'

同理：

import gmpy2 as gp
from Crypto.Util.number import long_to_bytes
p=9540203717217880059997385799331301649727503984010337568404427747385824530958536656147747848448822264268428226235860927158082497191830274046098671199542207
n2=0x9f159326c907441326c88d17eae1c6e8aaea23922c5e628a585294e379e9245644f9c249c57f54a2b83921b4adc988fecc90c00feb6936d9be1f3a5ffae951b74ffbc6fc7aa11743e4ca179a937392dacf931e820d1d83016562ff608e8c59ef7310654a09bbba4a0129f71dcb61bd9bef073bbb93bfcac4a7a2e81156dbb32d
c2=0x6240740d41a539a88634726cf0a791a87e02419c3c3e00dff62eba59e81a93fd04a59109e57f64fc375b9a321583b6fa133317eb5c4e6eb1e6f6d9a0b4ae6ff0c54423718811f7956cd63b7bf9c7f8e29f48dad8f05b63b71d6c5112d91864adba0d6bb342c67aee39ccd5e2a6928a8e4ab2248d29a0c990bae821b31b39b1f3
q=n2//p
phi=(p-1)*(q-1)
e=65537
d=gp.invert(e,phi)
m=pow(c2,d,n2)
print(long_to_bytes(m))
#iv=b'\xf5\xf6\xa8\x8b\x08U\xedG\xe0\xdew\x1c\xaf<\xb2>'

iv和key都已求出，进行最后一步。

import gmpy2 as gp
from Crypto.Cipher import AES
import binascii
key=b'\x89)\xef\x12\xa1\x7f\x14[\xc9\xb4\x8a\xfa,\x88\xa2\xef'
iv=b'\xf5\xf6\xa8\x8b\x08U\xedG\xe0\xdew\x1c\xaf<\xb2>'
aa = AES.new(key, AES.MODE_CBC, iv)
data = 'f8559d671b720cd336f2d8518ad6eac8c405585158dfde74ced376ba42d9fe984d519dc185030ddec7b4dc240fd90fa8'
data = binascii.a2b_hex(data)
data = aa.decrypt(data)
print(data)