P06.RSA密钥生成与读取

P06.RSA密钥生成与读取

1.pycryptodome模块

公钥生成

from Crypto.PublicKey import RSA

p= 787228223375328491232514653709
q= 814212346998672554509751911073
n= 640970939378021470187479083920100737340912672709639557619757
d= 590103645243332826117029128695341159496883001869370080307201
e= 65537


rsa_components = (n, e)
keypair = RSA.construct(rsa_components)
with open('pubckey.pem', 'wb') as f :
    f.write(keypair.exportKey())

私钥生成

from Crypto.PublicKey import RSA

p= 787228223375328491232514653709
q= 814212346998672554509751911073
n= 640970939378021470187479083920100737340912672709639557619757
d= 590103645243332826117029128695341159496883001869370080307201
e= 65537


rsa_components = (n,e,d,p,q)
keypair = RSA.construct(rsa_components)
with open('private1.pem', 'wb') as f :
    f.write(keypair.exportKey())

公钥读取

from Crypto.PublicKey import RSA
with open("pubckey.pem","rb") as f:
    key = RSA.import_key(f.read())
    print('n = %d' % key.n)
    print('e = %d' % key.e)

私钥读取

from Crypto.PublicKey import RSA
with open("private1.pem","rb") as f:
    key = RSA.import_key(f.read())
    print('n = %d' % key.n)
    print('e = %d' % key.e)
    print('d = %d' % key.d)
    print('p = %d' % key.p)
    print('q = %d' % key.q)

2.rsa模块 （不推荐）

公钥生成

import rsa

p= 787228223375328491232514653709
q= 814212346998672554509751911073
n= 640970939378021470187479083920100737340912672709639557619757
d= 590103645243332826117029128695341159496883001869370080307201
e= 65537

pubkey = rsa.PublicKey(n , e )
print(pubkey)
pub=rsa.PublicKey.save_pkcs1(pubkey)
with open("pub.pem","wb") as f:
    f.write(pub)

私钥生成

import rsa

p= 787228223375328491232514653709
q= 814212346998672554509751911073
n= 640970939378021470187479083920100737340912672709639557619757
d= 590103645243332826117029128695341159496883001869370080307201
e= 65537
prikey = rsa.PrivateKey(n , e , d , p , q)
print(prikey)
pri=rsa.PrivateKey.save_pkcs1(prikey)
with open("pri.pem","wb") as f:
    f.write(pri)

公钥读取

import rsa
with open('2.pem','rb') as f:
    keydata= f.read()
pubckey = rsa.PublicKey.load_pkcs1(keydata)
#pubckey = rsa.PublicKey.load_pkcs1_openssl_pem(keydata)
print(pubckey.n)
print(pubckey.e)

私钥读取

import rsa
with open('1.pem','rb') as f:
    keydata= f.read()
pubckey = rsa.PrivateKey.load_pkcs1(keydata)
print(pubckey.n)
print(pubckey.e)
print(pubckey.d)
print(pubckey.q)
print(pubckey.p)

出题脚本

随机生成flag

import random
import hashlib
import string

#字符串列表
a=string.printable
#随机生成flag
for i in range(10):
    flag = ""
    for i in range(10):
        flag += a[random.randint(0, 99)]
    flag = hashlib.md5(flag.encode()).hexdigest()
    print("flag{" + flag + "}")

基于N分解的题目

import libnum
import gmpy2
from Crypto.PublicKey import RSA

p=libnum.generate_prime(1024)
#下一个素数
q=int(gmpy2.next_prime(p))
e=65537
m="flag{a272722c1db834353ea3ce1d9c71feca}"
m=libnum.s2n(m)
n=p*q
c=pow(m,e,n)
flag_c=libnum.n2s(c)
rsa_components = (n, e)
keypair = RSA.construct(rsa_components)
with open('pubckey1.pem', 'wb') as f :
    f.write(keypair.exportKey())
with open("flag.txt","wb") as f:
    f.write(flag_c)

解题脚本

import libnum
import gmpy2
from Crypto.PublicKey import RSA


def isqrt(n):
  x = n
  y = (x + n // x) // 2
  while y < x:
    x = y
    y = (x + n // x) // 2
  return x

def fermat(n, verbose=True):
    a = isqrt(n) # int(ceil(n**0.5))
    b2 = a*a - n
    b = isqrt(n) # int(b2**0.5)
    count = 0
    while b*b != b2:
        # if verbose:
        #     print('Trying: a=%s b2=%s b=%s' % (a, b2, b))
        a = a + 1
        b2 = a*a - n
        b = isqrt(b2) # int(b2**0.5)
        count += 1
    p=a+b
    q=a-b
    assert n == p * q
    # print('a=',a)
    # print('b=',b)
    # print('p=',p)
    # print('q=',q)
    # print('pq=',p*q)
    return p, q


with open("pubckey1.pem","rb") as f:
    key = RSA.import_key(f.read())
    n=key.n
    e=key.e

with open("flag.txt","rb") as f:
    c=f.read()
    c=libnum.s2n(c)

#费马分解,
n1=fermat(n)
p=n1[0]
q=n1[1]
phi_n=(p-1)*(q-1)
#求逆元
d=libnum.invmod(e,phi_n)
m=pow(c,d,n)
print(m)
print(libnum.n2s(int(m)).decode())

自动生成密钥及加解密过程

from Crypto.Cipher import PKCS1_v1_5
from Crypto import Random
from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP


random_generator = Random.new().read
rsa = RSA.generate(2048, random_generator)
# 生成私钥
private_key = rsa.exportKey()
# print(private_key.decode('utf-8'))
with open('rsa_private_key.pem', 'wb')as f:
    f.write(private_key)
# 生成公钥
public_key = rsa.publickey().exportKey()
# print(public_key.decode('utf-8'))
with open('rsa_public_key.pem', 'wb')as f:
    f.write(public_key)


#测试用密钥加密
public_key = RSA.importKey(public_key)
msg='flag'
pk = PKCS1_v1_5.new(public_key)
encrypt_text = pk.encrypt(msg.encode())
print(encrypt_text)

#测试密钥解密
private_key = RSA.importKey(private_key)
pk = PKCS1_v1_5.new(private_key)
msg = pk.decrypt(encrypt_text,0)
print(msg)


#两种标准
rsa_components = (n, e, int(d), p, q)
arsa = RSA.construct(rsa_components)
rsakey = RSA.importKey(arsa.exportKey())
rsakey = PKCS1_OAEP.new(rsakey)
decrypted = rsakey.decrypt(c)
print(decrypted)