NSSCTF Round#11 --- 密码个人赛 wp

文章目录

- - ez_enc
  - MyMessage
  - MyGame
  - ez_signin
  - ez_fac

ez_enc

题目：

ABAABBBAABABAABBABABAABBABAAAABBABABABAAABAAABBAABBBBABBABBABBABABABAABBAABBABAAABBAABBBABABABAAAABBAAABABAABABBABBBABBAAABBBAABABAABBAAAABBBAAAABAABBBAABBABABAABABAAAAABBBBABAABBBBAAAABBBBBAB

将A替换为0，B替换为1，再二进制转字符串

在这里插入图片描述
flag:

NSSCTF{mS4gT1Kv9L8NjPzx}

MyMessage

题目：

from Crypto.Util.number import *
import os

flag = os.getenv('FLAG')

e = 127

def sign():
    msg = input("Input message：")
    p = getPrime(512)
    q = getPrime(512)
    n = p*q
    c = pow(bytes_to_long((msg + flag).encode()), e, n)
    print(f"n: {n}")
    print(f"Token: {hex(c)}")

def main():
    while True:
        sign()

main()

与黄河流域警校CTF类似，取127组数据构成 低加密指数广播攻击，之后按照板子解题即可

解题代码：

import gmpy2
from pwn import *
from functools import reduce
from Crypto.Util.number import *

def CRT(ai, mi):
    assert (reduce(gmpy2.gcd, mi) == 1)
    assert (isinstance(mi, list) and isinstance(ai, list))
    M = reduce(lambda x, y: x * y, mi)
    ai_ti_Mi = [a * (M // m) * gmpy2.invert(M // m, m) for (m, a) in zip(mi, ai)]
    return reduce(lambda x, y: x + y, ai_ti_Mi) % M

e = 127
n = []
c = []
for i in range(127):
    p = remote('node2.anna.nssctf.cn', 28949)
    message='1'
    send_data = p.sendline(message.encode())
    get_n = p.recvline().decode()
    get_token = p.recvline().decode()
    n_data = int(get_n.split(':')[1].replace('\n',''))
    c_data = int(get_token.split(':')[1].strip(),16)
    n.append(n_data)
    c.append(c_data)

M = int(CRT(c,n))
m = gmpy2.iroot(M,127)[0]
flag = long_to_bytes(m)
print(flag)

MyGame

题目：

from Crypto.Util.number import *
import os
import random
import string

flag = os.getenv('FLAG')

def menu():
    print('''=---menu---=
1. Guess
2. Encrypt
''')

p = getPrime(512)
q = getPrime(512)
n = p*q

def randommsg():
    return ''.join(random.choices(string.ascii_lowercase+string.digits, k=30))

mymsg = randommsg()
def guess():
    global mymsg
    msg = input()

    if msg == mymsg:
        print(flag)
    else:
        print(mymsg)
        mymsg = randommsg()

def encrypt():
    e = random.getrandbits(8)
    c = pow(bytes_to_long(mymsg.encode()), e, n)
    print(f'Cipher_{e}: {c}')

def main():
    print(f'n: {n}')
    while True:
        opt = int(input())

        if opt == 1:
            guess()
        elif opt == 2:
            encrypt()

main()

显然n已经确定了，那么直接取两组数据构成共模攻击，然后按照板子解题即可

解题代码：

from Crypto.Util.number import *
import gmpy2

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 deocode():
  n = 92376669002623921509402142523040417979742847285128913230222037277281193123569384917422295565460337201247419578329317570919388466167460921476436708744255861919569840646055365622736782018449981456970295507042507578400203506466228792516604670880411611388070363010575761687416199559859671498479577162814750167227
  c1 = 56209807203263700238616560618292167910103178762773040784631746817419178047868684355927134794504437622277771565804770934927080520866774097937077159522561456694970573720502644960107683432027702982653269325018244743399259436663458302138397221829147003127560773174189067496942399020628208697090961657373400555014
  c2 = 90201008191161333080317628432839944522494767331025005565907527059217108167006947509077285590701267614286437629784262846613850046677772564536135707131060135969549898546289759735024482099701063980172806975932382772513818194522857561088504530894222162124688966716463702313948548512256262573687696646070994545974
  e1 = 170
  e2 = 98
  s = egcd(e1, e2)
  s1 = s[1]
  s2 = s[2]
  if s1 < 0:
    s1 = - s1
    c1 = gmpy2.invert(c1, n)
  elif s2 < 0:
    s2 = - s2
    c2 = gmpy2.invert(c2, n)
  if gmpy2.gcd(e1, e2) == 1:
    print("e1,e2互质")
    message = pow(c1, s1, n) * pow(c2, s2, n) % n
    flag = long_to_bytes(message)
    print(flag)
  elif gmpy2.gcd(e1, e2) != 1:
    message = pow(c1, s1, n) * pow(c2, s2, n) % n
    common_e = gmpy2.gcd(e1, e2)
    print("e1,e2不互质，且公约数为" + str(common_e))
    flag = long_to_bytes((gmpy2.iroot(message, common_e)[0]))
    print(flag)


if __name__ == '__main__':
    deocode()

解密得到随机字符串:dpb3o4zvh47f8xksol7zgvbuullc96，之后选择1进入到guess()方法输入字符串即可得到flag 在这里插入图片描述

ez_signin

题目：

from Crypto.Util.number import *
from secret import flag

p = getPrime(512)
q = getPrime(512)
assert p > q
n = p*q
e = 65536
m = bytes_to_long(flag)
num1 = (pow(p,e,n)-pow(q,e,n)) % n
num2 = pow(p-q,e,n)
c = pow(m,e,n)

print("num1=",num1)
print("num2=",num2)
print("n=",n)
print("c=",c)

晚点写！！！！
解题代码：

from Crypto.Util.number import *
import gmpy2

num1= 134186458247304184975418956047750205959249518467116558944535042073046353646812210914711656218265319503240074967140027248278994209294869476247136854741631971975560846483033205230015783696055443897579440474585892990793595602095853960468928457703619205343030230201261058516219352855127626321847429189498666288452
num2= 142252615203395148320392930915384149783801592719030740337592034613073131106036364733480644482188684184951026866672011061092572389846929838149296357261088256882232316029199097203257003822750826537629358422813658558008420810100860520289261141533787464661186681371090873356089237613080052677646446751824502044253
n= 154128165952806886790805410291540694477027958542517309121222164274741570806324940112942356615458298064007096476638232940977238598879453357856259085001745763666030177657087772721079761302637352680091939676709372354103177660093164629417313468356185431895723026835950366030712541994019375251534778666996491342313
c= 9061020000447780498751583220055526057707259079063266050917693522289697419950637286020502996753375864826169562714946009146452528404466989211057548905704856329650955828939737304126685040898740775635547039660982064419976700425595503919207903099686497044429265908046033565745195837408532764433870408185128447965

p = GCD(num1+num2,n)
q = n//p

x0=gmpy2.invert(p,q)
x1=gmpy2.invert(q,p)
cs = [c]
for i in range(16):
    ps = []
    for c2 in cs:
        r = pow(c2, (p + 1) // 4, p)
        s = pow(c2, (q + 1) // 4, q)

        x = (r * x1 * q + s * x0 * p) % n
        y = (r * x1 * q - s * x0 * p) % n
        if x not in ps:
            ps.append(x)
        if n - x not in ps:
            ps.append(n - x)
        if y not in ps:
            ps.append(y)
        if n - y not in ps:
            ps.append(n - y)
    cs = ps

for m in ps:
    flag = long_to_bytes(m)
    if b"nssctf" in flag:
        print(flag)
        break

ez_fac

题目：

from Crypto.Util.number import *
import random
from secret import flag,a0,a1,b0,b1

p = getPrime(512)
q = getPrime(512)
e = getPrime(128)
n = p*q
assert pow(a0,2) + e * pow(b0,2) == n
assert pow(a1,2) + e * pow(b1,2) == n
m = bytes_to_long(flag)
c = pow(m,e,n)

print("c=",c)
print("n=",n)
print("a0=",a0)
print("a1=",a1)
print("b0=",b0)
print("b1=",b1)

当
$N=ma^2+nb^2$
$N = mc^2+nd^2$
则有， $\cdot \frac{N}{(N,ad-bc)}$
$那么, p = g c d (N, a d - b c)$
解题代码：

import gmpy2
from Crypto.Util.number import *

c= 34007465638566836660852768374211870538357285529060206826620688555044780516477877596651414637089490522614456532732711803500304737160162560168303462221485961593760966240770414498297915175227814336224871400766371471776600674705757656616409870237891336752248110367865552469248343708419900511716030176178698949179
n= 70043427687738872803871163276488213173780425282753969243938124727004843810522473265066937344440899712569316720945145873584064860810161865485251816597432836666987134938760506657782143983431621481190009008491725207321741725979791393566155990005404328775785526238494554357279069151540867533082875900530405903003
a0= 8369195163678456889416121467476480674288621867182572824570660596055739410903686466334448920102666056798356927389728982948229326705483052970212882852055482
a1= 8369195163678456889416121462308686152524805984209312455308229689034789710117101859597220211456125364647704791637845189120538925088375209397006380815921158
b0= 25500181489306553053743739056022091355379036380919737553326529889338409847082228856006303427136881468093863020843230477979
b1= 31448594528370020763962343185054872105044827103889010592635556324009793301024988530934510929565983517651356856506719032859
e = (n-pow(a0,2))//pow(b0,2)
p = gmpy2.gcd(a0*b1-a1*b0,n)
q = n//p
phi  = (p-1)*(q-1)
d = gmpy2.invert(e,phi)
m = pow(c,d,n)
flag = long_to_bytes(m)
print(flag)