Codegate 2018 Final / within2s

within2s / Crypto / 150pt

nc주소와 문제파일을 준다.

파일은 총 2개로 intro.txt는 프로그램이 시작될때 출력되는 banner이다. 소스코드 안에 안넣어서 소스코드가 깔끔해서 좋았다.

 ___       __   ___  _________  ___  ___  ___  ________     _______  ________      
|\  \     |\  \|\  \|\___   ___\\  \|\  \|\  \|\   ___  \  /  ___  \|\   ____\     
\ \  \    \ \  \ \  \|___ \  \_\ \  \\\  \ \  \ \  \\ \  \/__/|_/  /\ \  \___|_    
 \ \  \  __\ \  \ \  \   \ \  \ \ \   __  \ \  \ \  \\ \  \__|//  / /\ \_____  \   
  \ \  \|\__\_\  \ \  \   \ \  \ \ \  \ \  \ \  \ \  \\ \  \  /  /_/__\|____|\  \  
   \ \____________\ \__\   \ \__\ \ \__\ \__\ \__\ \__\\ \__\|\________\____\_\  \ 
    \|____________|\|__|    \|__|  \|__|\|__|\|__|\|__| \|__| \|_______|\_________\
                                                                       \|_________|

소스코드는 다음과 같다.

#!/usr/bin/python

from gmpy2 import *
import os
import sys
import time
import random
import struct
import string

prime = [1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999]

def PrintIntro():
    f = open("intro.txt", "rb")
    intro = f.read()
    f.close()
    print intro

def xgcd(b, n):
    x0, x1, y0, y1 = 1, 0, 0, 1
    while n != 0:
        q, b, n = b // n, n, b % n
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return  b, x0, y0

def GenerateP():
    for i  in xrange(10000):
        rint = random.randint(70,100)
        out = random.sample(prime,rint)
        out.append(2)
        out.sort()

        z = 1

        for j in xrange(len(out)):
            z = z*out[j]

        z = z + 1

        if is_prime(z, 50):
            return z

def GenerateN(randomST):
    p = GenerateP()
    q = next_prime(mpz_urandomb(randomST, 1024))

    # Prime Checking
    if is_prime(p, 50) and is_prime(q, 50):
        n = p*q
        return n

def msg_generator(size=50, chars=string.ascii_uppercase + string.digits + string.ascii_lowercase):
    return ''.join(random.choice(chars) for _ in range(size))

def EncryptMsg():
    msg = msg_generator()
    msgint = int(msg.encode('hex'),16)

    f = open("/dev/urandom")
    seed = f.read(8)
    f.close()
    randomST = random_state(struct.unpack(">Q", seed)[0])

    PrintIntro()
    print("[*] We are now Encrypting msg...")
    print("[*] Please wait for seconds.\n")
    sys.stdout.flush()

    e = 65537
    n = GenerateN(randomST)
    time.sleep(2)

    EncryptedData = powmod(msgint, e, n)

    print("[*] e : %d" % e)
    print("[*] n : %d\n" % n)
    print("[*] Encrypted Data : %d\n" % EncryptedData)
    sys.stdout.flush()

    print("[*] You have to decrypt msg within 2 seconds !!")
    print("    Then I will give you the Flag :D")
    print("    If not, you have to try one more time !!\n")

    print("[*] DECRYPT : ")
    sys.stdout.flush()

    recv_msg = raw_input()

    if recv_msg == msg:
        print "\n[*] Congratulations!!! Here is your Flag :)"
        sys.stdout.flush()
        os.system("cat flag")

if __name__ == '__main__':
    EncryptMsg()

처음에는 멍청하게 501개 소수에서 70개에서 100개 랜덤하게 뽑은다음에 다 곱하고 2도 곱해서 1더해가지고 p를 만들고 랜~~~덤한 q를 만들어서 N을 해서 RSA하길래...

p를 모두 구해서 딕셔너리를 만들어서 시도했다... 멍청하다...

import random
import struct
from gmpy2 import *

prime = [1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999]

def GenerateP():
    for i  in xrange(10000):
        rint = random.randint(70,100) # 70 ~ 100
        out = random.sample(prime,rint) # choice prime number in prime list rint value 
        out.append(2) # include out array 2
        out.sort() # sorting

        z = 1

        for j in xrange(len(out)):
            z = z*out[j]

        z = z + 1

        if is_prime(z, 50):
            return z

w = open("res.txt", 'a')
for i in range(0, 100000) :
    p = GenerateP()
    w.write(str(p) + '\n')

w.close()

물론 불가능하다.

그러다가 2시간쯤 삽질을 하곤 고딩때 알게 된 어떤 툴로 돌렸더니 N이 0.5초만에 p랑 q로 쪼개져나오는걸 보고 경악을 금치 못했다.

그리고 윈도우 GUI프로그램을 어떻게 Python에 붙일까 고민하고 선구한테 물어보고 하다가 결국 Python모듈을 찾기 시작했다. 하지만 여러 소스코드를 다해도 그 윈도우 툴보다는 한참느리다 못해 결과를 안보여주었다.

하지만 sympy.ntheory모듈에서 해당 작업을 해주는 것을 확인했다.

그런데 문제를 푸는 서버에는 python2와 python3이 설치되어있었고 이 둘은 서로 꼬여있었다.

pip로 모듈을 설치하면 python3에 설치가 되고 python(2) -m pip로 설치해도 python3에 설치가 되었으며 설치된걸 python2로 옮겨도 실행이 안되는 오류가 있었다. 물론 그것을 해결할 생각은 안했고 나도 코드로 꼬아서 해결했다.

최종 문제 풀이 코드는 다음과 같다.

Attack.py - Python2

from pwn import * import os import gmpy import math

def egcd(a, b): 
    x,y, u,v = 0,1, 1,0 
    while a != 0: 
        q, r = b//a, b%a 
        m, n = x-u_q, y-v_q 
        b,a, x,y, u,v = a,r, u,v, m,n 
        gcd = b 
    return gcd, x, y

p_con = remote("211.117.60.69", 8888)

value = p_con.recvuntil("[_] DECRYPT :") 
N = int(value.split("[_] n :")[1].split("\n")[0]) 
e = 65537 
msg = int(value.split("[*] Encrypted Data : ")[1].split("\n")[0])

print ("[+] Parsed N : %d" %N) os.system("python3 sym.py %d > values.txt" %N) value = open('values.txt', 'rb').read().split('\n')

p = int(value[0]) q = int(value[1]) phi = (p - 1) * (q - 1) gcd, a, b = egcd(65537, phi)

d = a 
print d

pt = pow(msg, d, N) 
flag = "%x" %int(pt) 
if len(flag) % 2 != 0 : 
    flag = '0' + flag 
print len(flag.decode('hex')) 
print flag.decode('hex') 
p_con.send(flag.decode('hex')+'\n') 
print p_con.recv(1024) 
print p_con.recv(1024) 
print p_con.recv(1024) 
p_con.close()

sym.py - Python3

import sympy from sympy.ntheory import factorint import sys

for i in factorint(int(sys.argv[1])).keys() : 
    print (i)

소스코드를 두개 놓고 python2랑 python3을 왔다 갔다 해서 해결했는데 조만간 서버는 포맷을 해야겠다.

[+] Opening connection to 211.117.60.69 on port 8888: Done
[+] Parsed N : 1672266681474782486321973558609133508360970173993284085908698763576675454610298678106119244144494637495339593425171376711818518986049904708494196667043696311909642233287272386009601493101307418958845691606460230728149728518824717422660215123581693377240526362121805536036566504966709603562411000320634292998813418881954979639395200030393380991484249675772637125342524739160366946080318583153965754337172334138985960320110754337137228405876446535330971883671962368637886341799436057827528329999750757961774656011175054761184157841962392843175721640522339241420006931873526663901533917327915084828150593018983140827386584145129
610657891283618329533812521241951616981166946976628084043623888946961212440814623257635316704549272388703589573083927971485432601036762736830845394749374248693433601279140069609255579793101441178618110251091844939287414787257780144942616664442331597481121761726948900444437639758659905587006119591580632315289605266341459942072815988929778335909083996969916079064258305490240586723970143588010500588412144770158417471142930650788288233193955360191570184954512357307854842962201134816300621784816448689139617029400413798211292797700477990673814617888112727662075315371665124040749375388983710263868602775366175352499930141873
50
wxyBjMZGXoR0aft4k6VzqI6tDhiwUarhFKOUjDcO9yABf2BIdA

[*] Congratulations!!! Here is your Flag :)

Flag{MATHEMATICS is re4lly interest!ng... isn't it?? I love it! :D}

[*] Closed connection to 211.117.60.69 port 8888

Flag{MATHEMATICS is re4lly interest!ng... isn't it?? I love it! :D}