本文介绍了在CTF比赛中密码学中常用的工具及python库：简要讲解了安装方法，常用的使用方法。
根据p，q生成私钥文件key.pem
python rsatool.py -f PEM -o key.pem -n 13826123222358393307 -d 9793706120266356337
<pre>Using (n, d) to initialise RSA instance
提供（p,q）生成key.der
python rsatool.py -f DER -o key.der -p 4184799299 -q 3303891593
<pre>Using (p, q) to initialise RSA instance
openssl可以查看公钥得到n和e，也可以利用私钥文件解密公钥加密的内容
查看公钥文件
openssl rsa -pubin -in pubkey.pem -text -modulus
解密
rsautl -decrypt -inkey private.pem -in flag.enc -out flag
本地对应pip安装即可：
pip3 install factordb-python
更新factordb-python
pip3 install --upgrade factordb-python
命令行使用
C:\Users\fishmouse>factordb 16
<pre>2 2 2 2</pre>
获得更多信息：
C:\Users\fishmouse>factordb --json 16
<pre>{"id": "912K9s2c8@1M7q4)9K6b7g2)9J5c8W2)9J5c8X3k6S2j5%4c8G2M7X3c8T1i4K6u0W2j5$3!0E0i4K6u0r3j5i4m8A6i4K6u0r3i4K6y4r3K9h3c8Q4x3@1b7J5 ", "status": "FF", "factors": [2, 2, 2, 2]}</pre>
FacotrDB库的使用
xxx\yafu-1.34> .\yafu-x64.exe
factor(21)
whl文件形式安装,下载对应python版本的whl文件：51dK9s2c8@1M7s2y4Q4x3@1q4Q4x3V1k6Q4x3V1k6%4N6%4N6Q4x3X3g2D9k6X3c8Q4x3X3g2#2j5$3W2Q4x3X3g2W2k6s2g2Q4x3V1k6Q4y4@1g2Y4L8$3S2D9K9$3g2Q4x3V1k6H3P5i4c8Z5L8$3&6D9K9h3u0K6i4K6u0r3
pip3 install gmpy2-2.0.8-cp37-cp37m-win_amd64.whl
安装gmpy2这个库还需要一些相应的环境mpfr和mpc
首先安装mpfr，因为要安装mpc必须先安装mpfr
root@kali:~# wget caaK9s2c8@1M7s2y4Q4x3@1q4Q4x3V1k6Q4x3V1k6%4N6%4N6Q4x3X3g2E0M7r3k6J5i4K6u0W2L8%4u0Y4i4K6u0r3L8i4m8X3M7W2)9J5k6r3y4#2M7Y4u0W2L8Y4c8Q4x3V1k6E0M7r3k6J5i4K6u0V1y4q4)9J5k6e0q4Q4x3X3f1H3i4K6u0W2N6r3q4J5i4K6u0W2j5Y4Z5J5
若失败到官网：738K9s2c8@1M7s2y4Q4x3@1q4Q4x3V1k6Q4x3V1k6%4N6%4N6Q4x3X3g2E0M7r3k6J5i4K6u0W2L8%4u0Y4i4K6u0r3L8i4m8X3M7W2)9J5k6r3y4#2M7Y4u0W2L8Y4c8Q4c8e0k6Q4z5f1k6Q4b7e0g2Q4c8e0N6Q4z5f1y4Q4z5p5u0Q4c8e0k6Q4z5f1y4Q4z5o6m8Q4c8e0k6Q4z5e0k6Q4b7U0l9`.
root@kali:~# tar -jxvf mpfr-4.1.0.tar.bz2
root@kali:~# cd mpfr-4.1.0
root@kali:~/mpfr-4.1.0# ./configure
root@kali:~/mpfr-4.1.0# make && make check && make install
安装mpc
root@kali:~# wget ftp://ftp.gnu.org/gnu/mpc/mpc-1.1.0.tar.gz
root@kali:~# tar -zxvf mpc-1.1.0.tar.gz && cd mpc-1.1.0
root@kali:~/mpc-1.1.0# ./configure
root@kali:~/mpc-1.1.0# make && make check && make install
安装gmpy2
root@kali:~# pip3 install gmpy2
pip3 install libnum
pip3 install pycryptodome
安装后，可以使用Crypto 这个模块，注意点：在对应python下的库Lib\site-packages中crypto开头为小写时，将其改为Crypto 即可
openssl rsa -pubin -in pubkey.pem -text -modulus
python rsatool.py -f PEM -o prvkey.pem -p 4184799299 -q 3303891593
OpenSSL> rsautl -decrypt -in test.enc -inkey private.pem
FactorDB存储了已经知道的整数的分解，这个工具可以在命令行上使用，对python2和python3也适用
FactorDB存储了已经知道的整数的分解，这个工具可以在命令行上使用，对python2和python3也适用
from factordb.factordb import FactorDB
f = FactorDB(16)
from factordb.factordb import FactorDB
f = FactorDB(16)
f.get_factor_list()
f.connect()
<Response [200]>
f.get_factor_list()
[2, 2, 2, 2]
f.get_factor_from_api()
[['2', 4]]
f.get_status()
'FF'
import gmpy2
gmpy2.gcd(2,4)
import gmpy2
gmpy2.gcd(2,4)
mpz(2)
gmpy2.invert(5,26)
mpz(21)
gmpy2.gcdext(5,26)
(mpz(1), mpz(-5), mpz(1))
(mpz(1), mpz(-5), mpz(1))
gmpy2.iroot(4,2)
(mpz(2), True)
import libnum
libnum.gcd(2,4)
import libnum
libnum.gcd(2,4)
2
libnum.invmod(5,26)
libnum.xgcd(5,26)
(-5, 1, 1)
libnum.s2n("hell0")
448378203184
libnum.n2s(448378203184)
'hell0'
import libnum
libnum.s2n("hello")
import libnum
libnum.s2n("hello")
448378203247
libnum.n2s(448378203247)
'hello'
from Crypto.Util.number import long_to_bytes,bytes_to_long
bytes_to_long('hello'.encode())
from Crypto.Util.number import long_to_bytes,bytes_to_long
bytes_to_long('hello'.encode())
448378203247
long_to_bytes(448378203247)
long_to_bytes(448378203247)
b'hello'
import random
def rabin_miller(num):
s = num - 1
t = 0
while s % 2 == 0:
s = s // 2
t += 1
for trials in range(5):
a = random.randrange(2, num - 1)
v = pow(a, s, num)
if v != 1:
i = 0
while v != (num - 1):
if i == t - 1:
return False
else:
i = i + 1
v = (v ** 2) % num
return True
def is_prime(num):
if num < 2:
return False
small_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
if num in small_primes:
return True
for prime in small_primes:
if num % prime == 0:
return False
return rabin_miller(num)
def get_prime(key_size=1024):
while True:
num = random.randrange(2**(key_size-1), 2**key_size)
if is_prime(num):
return num
print(get_prime(50))
import random
def rabin_miller(num):
s = num - 1
t = 0
while s % 2 == 0:
s = s // 2
t += 1
for trials in range(5):
a = random.randrange(2, num - 1)
v = pow(a, s, num)
if v != 1:
i = 0
while v != (num - 1):
if i == t - 1:
return False
else:
i = i + 1
v = (v ** 2) % num
return True
def is_prime(num):
if num < 2:
return False
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