pem类文件解析及2022蓝帽杯crypto详解

from Crypto.PublicKey import RSA
from Crypto.Util.number import *
p,q = getPrime(512),getPrime(512)
n = p * q
e = 0x10001
pub = RSA.construct((n,e))
with open('out.pem','wb') as f:
    f.write(pub.exportKey('PEM'))
with open('out.pem','rb') as f:
    print(f.read().decode())
'''
-----BEGIN PUBLIC KEY-----
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCuRPouMRTcLWPBEUlhjCrZ6MNQ
rSy29BrHjH4+lGMykB23azPtT9fk7IsEFXoodm6tsPL8kheJ6cP+0WPldlQOw/K3
c9LUGzeCCAhNJuBjUoeW32ruE2HS7RoIF6vkP36zLs167ZZMK7Fg0cqW6VNXoJHT
zaKdqysBe+3W1VHl6QIDAQAB
-----END PUBLIC KEY-----
'''

from Crypto.PublicKey import RSA
from Crypto.Util.number import *
p,q = getPrime(512),getPrime(512)
n = p * q
e = 0x10001
d = inverse(e,(p - 1) * (q - 1))
pub = RSA.construct((n,e,d,p,q))
with open('out.pem','wb') as f:
    f.write(pub.exportKey('PEM'))
with open('out.pem','rb') as f:
    print(f.read().decode())
'''
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
'''

from Crypto.PublicKey import RSA
from Crypto.Util.number import *
key = RSA.generate(1024)
print(key.publickey)
with open('out.pem','wb') as f:
    f.write(key.exportKey('PEM'))
with open('out.pem','rb') as f:
    print(f.read().decode())
'''
<bound method RsaKey.public_key of RsaKey(n=99929675131146107818047790971049703803161677332600984800831117021637597471437271599719384035180982326470249457001083005224626356572009901255841391966616564984242588913592789383087326511196585443834216472384770224810255153922375944881215835774119177009570247468911673932973239275741131654695253944455708641727, e=65537, d=27501740780061900509028777360107084282858928440567277451824014559115713670042546183199393779857817534085793587304881725189343016621314014739780326627796196251470626677550096120689732366473717193895036548926100990548453802714993577259273117223098888966957225092204230317866243049867167880710514827901086931493, p=9959145719455053414348729655771312861460726396890001110536788452571591154277537325754067618769136991544158484849077735057792084414015625760536769751415507, q=10033960536990122517580769502852456118641921945920255759007869111269242067226468943041901092934902353013133963062909073461567977701122665256982872188799461, u=2111771661302217183343493746406805348965531581492223651147849337466575464897027597797323383307376291792334461891498947953036261381547003770335520720819326)>
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
'''

from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP
from Crypto.Util.number import *
flag = b'This_is_a_message_qwer'

key = RSA.generate(1024)
pub = key.publickey().exportKey()
public_key = RSA.importKey(pub)
pk = PKCS1_OAEP.new(public_key)
enc = pk.encrypt(flag)
print(enc)

priv = key.exportKey()
priv_key = RSA.importKey(priv)
sk = PKCS1_OAEP.new(priv_key)
msg = sk.decrypt(enc)
print(msg)
b'\xd1/Ou\xae\xba]z\xc0\t\xc6\xd7\xc4f\x13\x96\x9a\xeb5\xdb8\x92\xc7\x19\x12y\x9c\x18\xf7A\x9d\xe9\n&=<\x16\x07\xefz\xad2-\x983\xec\x932\xcb\xf0\x87~\xdf\xc1\xd2\x9f\xd7@\\H\x1f\x87#\xf3\x84\xa0\xfc\xd9\xcfV$>\xd7Of\xe6G\x06\xcb\x91\xa1\xcc\x0c\xad\xc2\x9a\xad\xe46\x91x\xad\xa51\xbb\xfb\xc1E\x93~e%\xd1~\xf8l\x19n\x88\xff\xac^\xca\x8fs*}\xb9c0\xc0N\xf2\xfa\xa4\xd8\x18g'
b'This_is_a_message_qwer'

from Crypto.PublicKey import RSA
key = RSA.generate(1024)
with open('1.pem','wb') as f:
    f.write(b'n = ' + str(hex(key.n)[2:]).encode() + b'\n')
    f.write(b'e = ' + str(hex(key.e)[2:]).encode() + b'\n')
    f.write(b'p = ' + str(hex(key.p)[2:]).encode() + b'\n')
    f.write(b'q = ' + str(hex(key.q)[2:]).encode() + b'\n')
    f.write(b'd = ' + str(hex(key.d)[2:]).encode() + b'\n')
    f.write(b'dp = '+ str(hex((key.d) % ((key.p) - 1))[2:]).encode() + b'\n')
    f.write(b'dq = ' + str(hex((key.d) % ((key.q) - 1))[2:]).encode() + b'\n')
    f.write(b'p_q = ' + str(hex(pow(key.p,-1,key.q))[2:]).encode() + b'\n')
    f.write(b'q_p = ' + str(hex(pow(key.q, -1, key.p))[2:]).encode() + b'\n')
    f.write(key.exportKey('PEM'))

with open('1.pem','rb') as f:
    print(f.read().decode())

from Crypto.Util.number import *
from Crypto.PublicKey import RSA

e = 65537
flag = b'ACTF{...}'

while True:
    p = getPrime(1024)
    q = inverse(e, p)
    if not isPrime(q):
        continue
    n = p * q
    public = RSA.construct((n, e))
    with open("public.pem", "wb") as file:
        file.write(public.exportKey('PEM'))
    with open("flag", "wb") as file:
        file.write(long_to_bytes(pow(bytes_to_long(flag), e, n)))
    break

from Crypto.PublicKey import RSA
with open(r'public.pem', "r") as f:
    key = f.read()
    rsakey = RSA.importKey(key)
    n = rsakey.n
    e = rsakey.e

from Crypto.Util.number import *
import gmpy2
from Crypto.PublicKey import RSA
from tqdm import tqdm
with open(r'public.pem', "r") as f:
    key = f.read()
    rsakey = RSA.importKey(key)
    n = rsakey.n
    e = rsakey.e
with open('flag','rb') as f:
    c = f.read()
    c = bytes_to_long(c)
print(c)

for k in tqdm(range(1,1 << 16)):
    root = gmpy2.iroot(1 + 4 * k * n * e,2)
    if root[1] == True:
        p = (1 + root[0]) // (2 * k)
        assert n % p == 0
        q = n // p
        phi = (p - 1) * (q - 1)
        d = gmpy2.invert(e,phi)
        m = pow(c,d,n)
        print(long_to_bytes(m))
        break

from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP
from secret import flag

key = RSA.generate(1024)
open("flag.enc",'wb').write(PKCS1_OAEP.new(key.publickey()).encrypt(flag))
open('priv.pem','wb').write(key.exportKey('PEM'))

n = 0xd7152506aa9cec05e5335d6b46f5491407c3199fd51091f1f6030d3762b9e03f49c9dcdc075054e0cc148b974b41854bd93b4ee16a2a876ee62005e80ef806b7aa3b64b1bf9b1fa773e353d0cdb9ff9783ddd5f5e67499ad10f361e938d00b82a6a4c42a0535c5e76721798e86b45cd4b8d03b0d7e75c2be8766a1e843bdc641
e = 0x10001

_dq = 0xc90bcecf1cbab3358585e8a041d1b1
qinvp = 0xe3016cb3609c1d643c167439c3b938b881f4237f24860d3b1cb85a626d5ccd4726964e0f8270d6c4df9ebfebcc538e4ee5e1a7b7368ede51ec6ae917f78eb598

from Crypto.Util.number import *
import gmpy2
from tqdm import tqdm
from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP
n = 0xd7152506aa9cec05e5335d6b46f5491407c3199fd51091f1f6030d3762b9e03f49c9dcdc075054e0cc148b974b41854bd93b4ee16a2a876ee62005e80ef806b7aa3b64b1bf9b1fa773e353d0cdb9ff9783ddd5f5e67499ad10f361e938d00b82a6a4c42a0535c5e76721798e86b45cd4b8d03b0d7e75c2be8766a1e843bdc641
e = 0x10001
_dq = 0xc90bcecf1cbab3358585e8a041d1b1
t = 0xe3016cb3609c1d643c167439c3b938b881f4237f24860d3b1cb85a626d5ccd4726964e0f8270d6c4df9ebfebcc538e4ee5e1a7b7368ede51ec6ae917f78eb598
with open('flag.enc','rb') as f:
    c = f.read()
PR.<x> = PolynomialRing(Zmod(n))
dq = (2 ** 120 * x) + _dq
for k in tqdm(range(65537,55000,-1)):
    f = t * (e * dq - 1) ** 2 + k * (2 * t - 1) * (e * dq - 1) + t * k * k - k * k
    f = f.monic()
    root = f.small_roots(X=2^392,beta=0.4)
    if len(root) > 0:
        print(int(root[0]) * 2 ** 120 + _dq)
        break
#dq = 11263269100321843418340309033584057768246046953115325020896491943793759194249558697334095131684279304657225064156696057310019203890620314290203835007881649
#k = 59199  

from Crypto.Util.number import *
from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP
import base64
import gmpy2
with open("flag.enc","rb")as f:
    c = f.read()
dq = 11263269100321843418340309033584057768246046953115325020896491943793759194249558697334095131684279304657225064156696057310019203890620314290203835007881649
k = 59199
n = 0xd7152506aa9cec05e5335d6b46f5491407c3199fd51091f1f6030d3762b9e03f49c9dcdc075054e0cc148b974b41854bd93b4ee16a2a876ee62005e80ef806b7aa3b64b1bf9b1fa773e353d0cdb9ff9783ddd5f5e67499ad10f361e938d00b82a6a4c42a0535c5e76721798e86b45cd4b8d03b0d7e75c2be8766a1e843bdc641
e = 0x10001
q = int((e * dq - 1) // k + 1)
assert n % q == 0
p = int(n // q)
phi = (p - 1) * (q - 1)
d = int(gmpy2.invert(e,phi))
key = RSA.construct((n,e,d,p,q))
flag = PKCS1_OAEP.new(key)
flag = flag.decrypt(c)
print(flag)