BUUCTF Crypto [QCTF2018]Xman-RSA wp
这题其实还是挺麻烦的，首先先还原给的加密脚本如下：
from gmpy2 import is_prime
from os import urandom
import base64
def bytes_to_num(b):
return int(b.encode('hex'), 16)
def num_to_bytes(n):
b = hex(n)[2:-1]
b = '0' + b if len(b)%2 == 1 else b
return b.decode('hex')
def get_a_prime(l):
random_seed = urandom(l)
num = bytes_to_num(random_seed)
while true:
if is_prime(num):
break
num+=1
return num
def encrypt(s, e, n):
p = bytes_to_num(s)
p = pow(p, e, n)
return num_to_bytes(p).encode('hex')
def separate(n):
p = n % 4
t = (p*p) % 4
return t == 1
f = open('flag.txt', 'r')
flag = f.read()
msg1 = ""
msg2 = ""
for i in range(len(flag)):
if separate(i):
msg2 += flag[i]
else:
msg1 += flag[i]
p1 = get_a_prime(128)
p2 = get_a_prime(128)
p3 = get_a_prime(128)
n1 = p1*p2
n2 = p1*p3
e = 0x1001
c1 = encrypt(msg1, e, n1)
c2 = encrypt(msg2, e, n2)
print(c1)
print(c2)
e1 = 0x1001
e2 = 0x101
p4 = get_a_prime(128)
p5 = get_a_prime(128)
n3 = p4*p5
c1 = num_to_bytes(pow(n1, e1, n3)).encode('hex')
c2 = num_to_bytes(pow(n1, e2, n3)).encode('hex')
print(c1)
print(c2)
print(base64.b64encode(num_to_bytes(n2)))
print(base64.b64encode(num_to_bytes(n3)))
我们先来分析一下这个脚本，flag分为了两部分c1，c2用了不同的参数进行RSA加密，于是我们的目标就是解出n1，n2得到欧拉函数，我们可以看到n1，n2都用了p1这个参数，相当于我们只要得到n1和n2的值就可以通过gcd得到了。我们发现，n2和n3题目都给了base64的加密结果，我们只需要找到方法求解n1就可以了，我们再看看后面的加密脚本，密文就是n1这下思路就很清楚了。然后看到代码
c1 = num_to_bytes(pow(n1, e1, n3)).encode('hex')
c2 = num_to_bytes(pow(n1, e2, n3)).encode('hex')
可以很清楚的看到密文、模数相同，通过共模攻击就可以很轻易的解得n1的取值最后求得flag
不过这道题，题目给的num_to_bytes函数可能有的时候用不了，我还是用了long_to_bytes靠谱
下面给出整题脚本
from Crypto.Util.number import *
from gmpy2 import *
import base64
def bytes_to_num(b):
return int(b.encode('hex'), 16)
def num_to_bytes(n):
b = hex(n)[2:-1]
b = '0' + b if len(b)%2 == 1 else b
return b.decode('hex')
b1="PVNHb2BfGAnmxLrbKhgsYXRwWIL9eOj6K0s3I0slKHCTXTAUtZh3T0r+RoSlhpO3+77AY8P7WETYz2Jzuv5FV/mMODoFrM5fMyQsNt90VynR6J3Jv+fnPJPsm2hJ1Fqt7EKaVRwCbt6a4BdcRoHJsYN/+eh7k/X+FL5XM7viyvQxyFawQrhSV79FIoX6xfjtGW+uAeVF7DScRcl49dlwODhFD7SeLqzoYDJPIQS+VSb3YtvrDgdV+EhuS1bfWvkkXRijlJEpLrgWYmMdfsYX8u/+Ylf5xcBGn3hv1YhQrBCg77AHuUF2w/gJ/ADHFiMcH3ux3nqOsuwnbGSr7jA6Cw=="
b2="TmNVbWUhCXR1od3gBpM+HGMKK/4ErfIKITxomQ/QmNCZlzmmsNyPXQBiMEeUB8udO7lWjQTYGjD6k21xjThHTNDG4z6C2cNNPz73VIaNTGz0hrh6CmqDowFbyrk+rv53QSkVKPa8EZnFKwGz9B3zXimm1D+01cov7V/ZDfrHrEjsDkgK4ZlrQxPpZAPl+yqGlRK8soBKhY/PF3/GjbquRYeYKbagpUmWOhLnF4/+DP33ve/EpaSAPirZXzf8hyatL4/5tAZ0uNq9W6T4GoMG+N7aS2GeyUA2sLJMHymW4cFK5l5kUvjslRdXOHTmz5eHxqIV6TmSBQRgovUijlNamQ=="
n2=bytes_to_num(base64.b64decode(b1))
n3=bytes_to_num(base64.b64decode(b2))
cn1=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
cn2=0x42ff1157363d9cd10da64eb4382b6457ebb740dbef40ade9b24a174d0145adaa0115d86aa2fc2a41257f2b62486eaebb655925dac78dd8d13ab405aef5b8b8f9830094c712193500db49fb801e1368c73f88f6d8533c99c8e7259f8b9d1c926c47215ed327114f235ba8c873af7a0052aa2d32c52880db55c5615e5a1793b690c37efdd5e503f717bb8de716303e4d6c4116f62d81be852c5d36ef282a958d8c82cf3b458dcc8191dcc7b490f227d1562b1d57fbcf7bf4b78a5d90cd385fd79c8ca4688e7d62b3204aeaf9692ba4d4e44875eaa63642775846434f9ce51d138ca702d907849823b1e86896e4ea6223f93fae68b026cfe5fa5a665569a9e3948a
e1 = 0x1001
e2 = 0x101
def gongmogongji(n, c1, c2, e1, e2):
def egcd(a, b):
if b == 0:
return a, 0
else:
x, y = egcd(b, a % b)
return y, x - (a // b) * y
s = egcd(e1, e2)
s1 = s[0]
s2 = s[1]
if s1 < 0:
s1 = - s1
c1 = invert(c1, n)
elif s2 < 0:
s2 = - s2
c2 = invert(c2, n)
m = pow(c1, s1, n) * pow(c2, s2, n) % n
return m
result = gongmogongji(n3, cn1, cn2, e1, e2)
n1=result
p1=gcd(n1,n2)
p2=n1//p1
p3=n2//p1
phi1=(p1-1)*(p2-1)
phi2=(p1-1)*(p3-1)
c1="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"
c2="129d5d4ab3f9e8017d4e6761702467bbeb1b884b6c4f8ff397d078a8c41186a3d52977fa2307d5b6a0ad01fedfc3ba7b70f776ba3790a43444fb954e5afd64b1a3abeb6507cf70a5eb44678a886adf81cb4848a35afb4db7cd7818f566c7e6e2911f5ababdbdd2d4ff9825827e58d48d5466e021a64599b3e867840c07e29582961f81643df07f678a61a9f9027ebd34094e272dfbdc4619fa0ac60f0189af785df77e7ec784e086cf692a7bf7113a7fb8446a65efa8b431c6f72c14bcfa49c9b491fb1d87f2570059e0f13166a85bb555b40549f45f04bc5dbd09d8b858a5382be6497d88197ffb86381085756365bd757ec3cdfa8a77ba1728ec2de596c5ab"
e = 0x1001
d1=invert(e,phi1)
d2=invert(e,phi2)
cipher1=bytes_to_num(c1.decode('hex'))
cipher2=bytes_to_num(c2.decode('hex'))
m1=long_to_bytes(pow(cipher1,d1,n1))
m2=long_to_bytes(pow(cipher2,d2,n2))
print m1,m2
flag=""
for i in range(100):
if(i%2==0):
flag+=m1[i//2]
else :
flag+=m2[(i-1)//2]
print flag
#XMAN{CRYPT0_I5_50_Interestingvim rsa.py}