Lorlike's Blog

发表于 更新于 分类于

crypto

Hardcore

模2同余方程组

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from pwn import *

def foo(l):
    return ''.join([str(i) for i in l])

import numpy as np
a=np.identity(256,dtype=np.int64)

r=remote('ctf.b01lers.com',9003)
r.sendline('1')
s=b''
r.recvuntil('answer.\n')
for i in range(256):
    print(i,s)
    r.sendline(foo(a[i]))
    s+=r.recvline().strip()
print(s)
r.interactive()
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from Crypto.Util.number import *

a=0b0110001001100011011101000110011001111011011001000110111101011111011110010110111101110101010111110110110001101001011010110110010101011111011010000110000101110010011001000110001101101111011100100110010101011111011000110110100001100001011011000111001101111101
print(long_to_bytes(a))
# bctf{do_you_like_hardcore_chals}

发表于 更新于 分类于

crypto

easy_real

爆破hash，xor密码

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from Crypto.Util.number import *
import hashlib
from pwn import *


h='37693cfc748049e45d87b8c7d8b9aacd'
n=4197356622576696564490569060686240088884187113566430134461945130770906825187894394672841467350797015940721560434743086405821584185286177962353341322088523
c=3298176862697175389935722420143867000970906723110625484802850810634814647827572034913391972640399446415991848730984820839735665233943600223288991148186397


for i in range(1,100):
    if hashlib.md5(str(i).encode()).hexdigest()==h:
        e=i

p = 64310413306776406422334034047152581900365687374336418863191177338901198608319
q=n//p

d=inverse(e,(p-1)*(q-1))
m=pow(c,d,n)
m=long_to_bytes(m)
l=len(m)
for i in range(1,10):
    a=bytes([i]*l)
    a=xor(a,m)
    if b'flag' in a:
        print(a)
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发表于 更新于 分类于

ezRSA

方法1

p,q的900位以后的高位hb都是一样的，可以先求出来

设\(p=hb+y\)，那么\(q=hb+2^{900}-y+z\)，z为300位的随机数，可以得到 \[ p+q=2hb+2^{900}+z,\ p-q=2y-2^{900}-z \] 因为\(n=pq\)，\(p+q\)的高位（低300位未知）已知，可以由\(p-q=\sqrt{(p+q)^2-4n}\)求出\(p-q\)的近似值相应的y的近似值也能求出，再用coppersmith求出y的低位从而求出p

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发表于 更新于 分类于

速查

LLL算法

\[ ||v_1|| ≤ ||v_2|| ≤ ... ≤ ||v_i|| ≤ 2^{ \frac{n(n−1)}{4(n+1−i)}}det(L)^{\frac{1}{n+1−i}}\\ ||v_1|| ≤ 2^{ \frac{n−1}{4}}det(L)^{\frac{1}{n}} \] #### Minkowski定理

格子L存在向量 \(v\) ，满足 \(||v||\le \sqrt{n}\ det(L)^\frac{1}{n}\)

CopperSmith算法

sage自带

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n=10001
P.<x> = PolynomialRing(Zmod(n))
f=x^3 + 10*x^2 + 5000*x - 222
f.small_roots(X=10)

参数见 sage doc

多元coppersmith脚本

脚本参考 coppersmith 参数：

  • f 函数
  • bounds 各变量的上界X组成的元组tuple
  • m 模的幂
  • d variable shifts（多元时要手动设置为f的项的个数）
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发表于 更新于 分类于

d3factor

方法1

造格子 设\(\epsilon=d_2-d_1\)，有 \(e_1e_2\epsilon +e_2-e_1\equiv0\ mod\ p^6\) 化为\(\epsilon+b=kp^6,\ b\equiv(e_1e_2)^{-1}(e_2-e_1)\ mod\ p^6\) 设\(M=N^{\frac{1}{2}}\)， \(L=\begin{pmatrix}M&b\\\\ 0&N\end{pmatrix}\) \((pq\ -k)L=(pqM\ -pq\epsilon)\)

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