常见的RSA套路脚本

工具

• rsatool https://github.com/ius/rsatool
• factordb（分解大素数） http://www.factordb.com
• python-PyCrypto库
• Openssl

解析加密密钥：

openssl rsa -pubin -text -modulus -in pub.key

生成解密密钥：

python rsatool.py -f PEM -o key.key -p 1 -q 1 -e 1

openssl rsautl -decrypt -inkey key.pem -in flag.enc -out flag

脚本生成解密密钥：

# coding=utf-8
import math
import sys
from Crypto.PublicKey import RSA

keypair = RSA.generate(1024)
keypair.p = 
keypair.q = 
keypair.e = 
keypair.n = keypair.p * keypair.q
Qn = long((keypair.p - 1) * (keypair.q - 1))

i = 1
while (True):
    x = (Qn * i) + 1
    if (x % keypair.e == 0):
        keypair.d = x / keypair.e
        break
    i += 1
private = open('private.pem', 'w')
private.write(keypair.exportKey())
private.close()

RSA套路

给出e,p,q,c

import gmpy2 as gp
import binascii
p =  gp.mpz()
q =  gp.mpz()
e =  gp.mpz()
c =  gp.mpz()
n = p*q
phi = (p-1) * (q-1)
d = gp.invert(e, phi)
m = pow(c, d, n)
print(m)

给出e,n,dp,c

import gmpy2 as gp

e = 
n = gp.mpz()
dp = gp.mpz()
c = gp.mpz()

for x in range(1, e):
    if(e*dp%x==1):
        p=(e*dp-1)//x+1
        if(n%p!=0):
            continue
        q=n//p
        phin=(p-1)*(q-1)
        d=gp.invert(e, phin)
        m=gp.powmod(c, d, n)
        if(len(hex(m)[2:])%2==1):
            continue
        print('--------------')
        print(m)
        print(hex(m)[2:])
        print(bytes.fromhex(hex(m)[2:]))

给出p,q,dp,dq,c

import gmpy2 as gp

p = gp.mpz()
q = gp.mpz()
dp = gp.mpz()
dq = gp.mpz()
c = gp.mpz()

n = p*q
phin = (p-1)*(q-1)
dd = gp.gcd(p-1, q-1)
d=(dp-dq)//dd * gp.invert((q-1)//dd, (p-1)//dd) * (q-1) +dq
print(d)

m = gp.powmod(c, d, n)
print('-------------------')
print(m)
print(hex(m)[2:])

低解密指数攻击（e长度较大）

import  RSAwienerHacker
n=
e=
d =  RSAwienerHacker.hack_RSA(e,n)
if d:
    print(d)
import hashlib
flag = "flag{" + hashlib.md5(hex(d)).hexdigest() + "}"
print flag

共模攻击（n,m相同,c,e不同）

from libnum import n2s,s2n
from gmpy2 import invert
def egcd(a, b):
  if a == 0:
    return (b, 0, 1)
  else:
    g, y, x = egcd(b % a, a)
    return (g, x - (b // a) * y, y)

def main():
  n = 
  c1 = 
  c2 = 
  e1 = 
  e2 = 
  s = egcd(e1, e2)
  s1 = s[1]
  s2 = s[2]
  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
  print hex(m)

if __name__ == '__main__':
  main()

e,m相同，存在两个n有公约数

import gmpy2
from gmpy2 import invert, iroot
import gmpy2 as gp
from libnum import xgcd, invmod

n=[,,,,,,,,,,,,,,,,,,,]
for i in n:
    for j in n:
        if (i<>j):
            pub_p=gmpy2.gcdext(i,j)
            if (pub_p[0]<>1)&(i>j):
                print i
                print j
                print pub_p[0]
                a=i,p=pub_p[0]
q=a/p
p =  gp.mpz()
q =  gp.mpz()
e =  gp.mpz()
c =  gp.mpz()
n = p*q
phi = (p-1) * (q-1)
d = gp.invert(e, phi)
m = pow(c, d, n)
print hex(m)

coppersmith定理攻击

只有部分高位的p或q，例如

p=0xBCF6D95C9FFCA2B17FD930C743BCEA314A5F24AE06C12CE62CDB6E8306A545DE468F1A23136321EB82B4B8695ECE58B763ECF8243CBBFADE0603922C130ED143D4D3E88E483529C820F7B53E4346511EB14D4D56CB2B714D3BDC9A2F2AB655993A31E0EB196E8F63028F9B29521E9B3609218BA0000000000000000000000000

参考https://www.52pojie.cn/thread-653446-1-8.html