[LitCTF 2023]babyLCG

题目分数：463

题目评分：

1.5

题目标签： RSALCG

题目描述：

- 题目描述:主打一个baby难度的LCG
- 出题人：3tefanie丶zhouflag以NSSCTF{}形式提交

题目附件：

附件信息

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

m = bytes_to_long(flag)
bit_len = m.bit_length()
a = getPrime(bit_len)
b = getPrime(bit_len)
p = getPrime(bit_len+1)

seed = m
result = []
for i in range(10):
    seed = (a*seed+b)%p
    result.append(seed)
print(result)
"""
result = [699175025435513913222265085178805479192132631113784770123757454808149151697608216361550466652878, 193316257467202036043918706856603526262215679149886976392930192639917920593706895122296071643390, 1624937780477561769577140419364339298985292198464188802403816662221142156714021229977403603922943, 659236391930254891621938248429619132720452597526316230221895367798170380093631947248925278766506, 111407194162820942281872438978366964960570302720229611594374532025973998885554449685055172110829, 1415787594624585063605356859393351333923892058922987749824214311091742328340293435914830175796909, 655057648553921580727111809001898496375489870757705297406250204329094679858718932270475755075698, 1683427135823894785654993254138434580152093609545092045940376086714124324274044014654085676620851, 492953986125248558013838257810313149490245209968714980288031443714890115686764222999717055064509, 70048773361068060773257074705619791938224397526269544533030294499007242937089146507674570192265]
"""

解题：

本人在Visual Studio Code里面跑的

建一个文件LitCTF-LCG，里面两个py，如下：

enc.py:

import uuid
from Crypto.Util.number import *

flag = f"MUMU11{{{uuid.uuid4()}}}"
seed = bytes_to_long(flag.encode())
length = seed.bit_length()
print(length)

a = getPrime(length)
b = getPrime(length)
m = getPrime(length)

results = []
for _ in range(10):
    seed = (a * seed + b) % m
    results.append(seed)

print(f"results = {results}")

main.py:

import sympy
import libnum
import contextlib


def lcg_get_m(output):
    t = [output[i] - output[i - 1] for i in range(1, len(output))]
    return [int(sympy.gcd(t[i + 3] * t[i + 1] - t[i + 2] * t[i + 2], t[i + 2] * t[i] - t[i + 1] * t[i + 1])) for i in range(len(t) - 3)]

def lcg_get_a(output, m):
    lis = []
    with contextlib.suppress(Exception):
        lis.extend((output[i + 2] - output[1]) * int(sympy.mod_inverse((output[i + 1] - output[i]), m)) % m for i in range(len(output) - 2))
    return lis

def lcg_get_b(output, a, m):
    return [(output[i] - a * output[i-1]) % m for i in range(1, len(output))]

def lcg_get_seed(output, a, b, m):
    with contextlib.suppress(Exception):
        a_inv = int(sympy.mod_inverse(a, m))
        return a_inv * (output[0] - b) % m

def lcg_solver(output, isPrint=True, isSet=False):
    lis = []
    for m in lcg_get_m(output):
        for a in lcg_get_a(output, m):
            for b in lcg_get_b(output, a, m):
                if (seed := lcg_get_seed(output, a, b, m)):
                    lis.append(seed)

    if isSet:
        lis = list(set(lis))
            
    if isPrint:
        for seed in lis:
            print(libnum.n2s(seed))
    return lis

if __name__ == '__main__':
    #这里是题目给出的输出列表
    output = [699175025435513913222265085178805479192132631113784770123757454808149151697608216361550466652878, 193316257467202036043918706856603526262215679149886976392930192639917920593706895122296071643390, 1624937780477561769577140419364339298985292198464188802403816662221142156714021229977403603922943, 659236391930254891621938248429619132720452597526316230221895367798170380093631947248925278766506, 111407194162820942281872438978366964960570302720229611594374532025973998885554449685055172110829, 1415787594624585063605356859393351333923892058922987749824214311091742328340293435914830175796909, 655057648553921580727111809001898496375489870757705297406250204329094679858718932270475755075698, 1683427135823894785654993254138434580152093609545092045940376086714124324274044014654085676620851, 492953986125248558013838257810313149490245209968714980288031443714890115686764222999717055064509, 70048773361068060773257074705619791938224397526269544533030294499007242937089146507674570192265]
    lcg_solver(output, isPrint=True, isSet=False)
    

跑主函数得到LitCTF{31fcd7832029a87f6c9f760fcf297b2f}