1=107 k
2=101 e
3=121 y
4=58 :
5=97 a
6=52 4
7=54 6
8=100 d
9=99 c
10=55 7
11=56 8
12=100 d
13=48 0
14=55 7
15=57 9
16=56 8
17=99 c
18=56 8
19=51 3
=52 4
20=52 4
XH想要给YF发送一个重要文件,为了不被他人窃取到,XH向YF索要了他的公钥文件信息。
YF将他现在使用的公钥发送给了XH:
-----BEGIN PUBLIC KEY-----
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQC0XAw5rV1kqGzeJ1SDB5pTkgO9
RSBgCPm0l5DtdXUDGIJ3dbVC6TOQUHSNFrJPB6AeaSqagyfQCVSUv2EzO/3PLvox
b7hxazHIA2eMZiM3sHcIV9RTdx9pJorDUSB2fV9cnQUiK2smr8X1dt9RCmygpSCf
Ny0ZUYq3DfP/HuErmQIDAQAB
-----END PUBLIC KEY-----
XH用公钥对这个重要的文件进行了加密,然后将密文文件发送给YF:
UtowVjnLpRLTx2oBQlLKDP5cSfvXsz5RB/zO7nqfT6V3wgyK04JOXppCCY/p55rONh2+AZ7NAm3wvu4UwKwZxnw7qtRDSRL6bGZISyrJnyjEXfZHcOSf5BNcjQkJQYRbfN85Z3Ycg+84ABdF+jP7ekQaYikp2duqCoFBJYQcOWw=
但是XH没想到HZ那居然存有YF一组以前用过的私钥信息{n,e,d}:
{126652791247329858012081502617335427176078480967667235544422134698198761482081791188813953951941166617081546172312960216751960777234759603468040766428093969369837780011477003514642408424390144176644572101310535367720328881391192872513206457534291258525724324556727750428833407076738446023533405981578792872857,11666173,78440145437642026565505218176077635100043568658968467746538509828225145179636090827892006864282536091633117590477854513613339188289472952126032503980856086589942743747087799102224535294351908895347839402204845161252154330813186873353157721693911405483196449338177610947843869107506937519564559825768669662629}
就这样,XH发送的文件泄露了。
XH发送给YF的信息即为key文件信息。
# coding=utf-8
import random
import libnum
d = 78440145437642026565505218176077635100043568658968467746538509828225145179636090827892006864282536091633117590477854513613339188289472952126032503980856086589942743747087799102224535294351908895347839402204845161252154330813186873353157721693911405483196449338177610947843869107506937519564559825768669662629
e = 11666173
n = 126652791247329858012081502617335427176078480967667235544422134698198761482081791188813953951941166617081546172312960216751960777234759603468040766428093969369837780011477003514642408424390144176644572101310535367720328881391192872513206457534291258525724324556727750428833407076738446023533405981578792872857
k = e * d - 1
r = k
t = 0
while True:
r = r // 2
t += 1
if r % 2 == 1:
break
success = False
for i in range(1, 101):
g = random.randint(0, n)
y = pow(g, r, n)
if y == 1 or y == n - 1:
continue
for j in range(1, t):
x = pow(y, 2, n)
if x == 1:
success = True
break
elif x == n - 1:
continue
else:
y = x
if success:
break
else:
continue
if success:
p = libnum.gcd(y - 1, n)
q = n // p
print('P: ' + '%s' % p)
print('Q: ' + '%s' % q)
else:
print('Cannot compute P and Q')
# -*- coding: utf-8 -*-
from Crypto.Util import number
import random
import gmpy2
from Crypto.Util.number import *
from secret import key
N = 21950613536281390486175757463951027643556662621824579929664918617520636813458994325720569579695736856079459340474316751889021883755540017377473409564797843019125596929359598746535191841338208989879009508321774759757392464348925062704618198548398309908878380041795632951630513476281083426748653263731919122841901104123145297521411331174923397782111024006706017326210374498919922250769088886696170966869394222786903527353128540253585182758832324462426318387914150570168191590734053846371944717431858873198597415498765665035309188308408227521317670668417094970551798085092238594309838065757300622761550073415879726501051
e = 0x10001
m = number.bytes_to_long(key)
with open('key.enc', 'w') as f:
while m:
p = getPrime(8)
padding = random.randint(0, 2**1000) ** 2
message = padding << m**(p-1) % p + m % 2
cipher = pow(message, e, N)
f.write(hex(cipher)+'\n')
m /= 2
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import gmpy2
N = 21950613536281390486175757463951027643556662621824579929664918617520636813458994325720569579695736856079459340474316751889021883755540017377473409564797843019125596929359598746535191841338208989879009508321774759757392464348925062704618198548398309908878380041795632951630513476281083426748653263731919122841901104123145297521411331174923397782111024006706017326210374498919922250769088886696170966869394222786903527353128540253585182758832324462426318387914150570168191590734053846371944717431858873198597415498765665035309188308408227521317670668417094970551798085092238594309838065757300622761550073415879726501051
e = 0x10001
invert2 = pow(gmpy2.invert(2,N),e,N)
with open('key.enc', 'r') as f:
l = f.read().split("\n")
byte = ""
flag = ""
for c in l:
if len(c) > 2:
c = int(c[2:-1], 16)
if gmpy2.jacobi(c * invert2, N) == -1:
byte = "1" + byte
else:
byte = "0" + byte
if len(byte) == 8:
flag = chr(int(byte, 2)) + flag
byte = ""
flag = chr(int(byte, 2)) + flag
print(flag)