作为练手的 160 个 CrackMe 系列整理分析
CrackMe 来源：【反汇编练习】160个CrackME索引目录1~160建议收藏备用
第二版的 CrackMe，有了 052 作铺垫后，053 就稍微轻松点了(并不)。053 的过程和前一个类似，同样先取用户名、产品 ID 等生成一个字符串并计算散列; 取序列号进行计算后两者进行对比，相同则通过。
散列这里就直接跳过不说了，这次不是 MD5，但是看看生成的结果是 128 位的似乎又不是 SHA-1 之类的，可能是修改了的 MD5。
直接看序列号的处理，看看能否找到算法的逆(应该要能)。计算的函数位于 0x00401AD0，其中 0x00401AB0 这个小函数的作用是计算 32 位整数比特位为 1 的 数量。这里直接贴上稍作整理后的 c 代码。
unsigned char countb(DWORD dw)
{
int count = 0;
while (dw)
{
++count;
dw &= dw - 1;
}
return count;
}
void func_401AD0(int *key, DWORD *addr1, DWORD *addr2)
{
int k0 = 0, k1 = 0;
for (int i = 0; i < 32; ++i)
{
unsigned char c1 = countb(*addr1 & key[0]);
unsigned char c2 = countb(*addr2 & key[1]);
++addr1;
++addr2;
k0 = (c1 ^ c2) & 1 ^ 2 * k0;
}
for (int i = 0; i < 32; ++i)
{
unsigned char c1 = count_bits(*addr1 & key[0]);
unsigned char c2 = count_bits(*addr2 & key[1]);
++addr1;
++addr2;
k1 = (c1 ^ c2) & 1 ^ 2 * k1;
}
key[0] = k0;
key[1] = k1;
}
这次的算法并不直观，首先是一对 key 分别和固定数值（addr1、addr2）作与运算，两者的结果计算非零位的数量后再异或。整体来看就是计算结果(两个 dword)的 64 个 bit 分别由 key 和 64 个固定的 dword 计算后填充，每次结果填充一个位，互不干扰。
一开始我盯着看了好久都没个想法……后来感觉这 64 个位独立计算和矩阵有点类似。可以这样看 countb(d1 & d2)：
例如 d1 = 0x12345678，d2 = 0x9abcdef0，那么
d1 00010010001101000101011001111000
&
d2 10011010101111001101111011110000
--------------------------------------
00010010001101000101011001110000
注意到 & 运算等价于模 2 乘，同样 ^ 运算等价于模 2 加，见模 2 运算。而 countb 则将结果中的所有 1 和 0 相加。
然后就有 countb(d1 & d2) = ∑(i=0,31){d1:i * d2:i}，其中 d1:i 表示 d1 的第 i 位。
所以
k1:m = ∑(i=0,31){key0:i * addr1[m]:i} +
∑(i=0,31){key1:i * addr2[m]:i}
如果把 key0,key1 看作一个 64 位整数，那么根据上面的公式可以这样安排一个矩阵：
x = [ x0:31, x0:30, ..., x0:0, x1:31, ..., x1:0 ]
A = ┌ ┐
│ addr1[0]:31, addr1[1]:31, ..., addr1[63]:31 │
│ addr1[0]:30, addr1[1]:30, ..., addr1[63]:30 │
│ . . │
│ . . │
│ addr1[0]:1 , ..., addr1[63]:1 │
│ addr1[0]:0 , ..., addr1[63]:0 │
│ addr2[0]:31, ..., addr2[63]:31 │
│ . , ..., . │
│ addr2[0]:0 , ..., addr2[63]:0 │
└ ┘
b = [ key0:31, key0:30, ..., key0:0, key1:31, ..., key1:0 ]
因为 key 是最后的计算结果，所以这样安排计算式：x * A = b，x0，x1 即代码中初始的 key[0]，key[1]。根据矩阵的乘法公式，这样 x 对应位置上的比特便能与 addr 上对应的比特相乘。
最后照着顺序（先 key[1]key[2]，再 key[0]key[1]）解出矩阵的解后即得到初始的序列号。矩阵运算找一个合适的数学库就好了。
#include <array>
#include "NTL/ZZ.h" // 用了 NTL 库
#include "NTL/vec_GF2.h"
#include "NTL/mat_GF2.h"
using namespace NTL;
const std::array<const unsigned char, 256> addr_0x41c2c0 = {
0x35, 0xEF, 0xCF, 0x0B, 0x6B, 0xDE, 0x9F, 0x17, 0x98, 0xE7, 0xE7, 0xC5, 0xAC, 0x79, 0x7F, 0x5E,
0x59, 0xF3, 0xFE, 0xBC, 0xB7, 0xC6, 0xFD, 0xF9, 0x6A, 0xAD, 0xFB, 0x73, 0xD6, 0xBC, 0x3F, 0x2F,
0xD5, 0x5A, 0xF7, 0xE7, 0xAF, 0x95, 0xEE, 0x4F, 0x5E, 0x2B, 0xDD, 0x9F, 0x76, 0xCD, 0x74, 0xFF,
0xB9, 0x76, 0xBA, 0xBF, 0xE8, 0xBA, 0xE9, 0x7E, 0xD1, 0x75, 0xD3, 0xFD, 0x4E, 0x97, 0x4D, 0xF7,
0xA7, 0xCB, 0xA6, 0x7B, 0x99, 0x0E, 0x9B, 0x6E, 0x32, 0x1D, 0x36, 0xDD, 0x60, 0x1A, 0x6C, 0x3A,
0xC0, 0x34, 0xD8, 0x74, 0x81, 0x69, 0xB0, 0xE9, 0x06, 0xF3, 0x60, 0x53, 0x0C, 0xE6, 0xC1, 0xA6,
0x1D, 0xEC, 0x83, 0xCD, 0x3F, 0xF8, 0x07, 0x1B, 0x7E, 0xF0, 0x0F, 0x36, 0xFD, 0xE0, 0x1F, 0x6C,
0xFA, 0xC1, 0x3F, 0xD8, 0xF0, 0xA3, 0x7F, 0x30, 0xE1, 0x47, 0xFF, 0x60, 0xC2, 0x8F, 0xFE, 0xC1,
0x80, 0x3F, 0xFD, 0x03, 0x02, 0xFE, 0xF4, 0x0F, 0x01, 0x7F, 0xFA, 0x07, 0x04, 0xFC, 0xE9, 0x1F,
0x08, 0xF8, 0xD3, 0x3F, 0x10, 0xF0, 0xA7, 0x7F, 0x47, 0xE0, 0x9F, 0x7E, 0x8E, 0xC0, 0x3F, 0xFD,
0x21, 0xE0, 0x4F, 0xFF, 0x32, 0x42, 0xFF, 0xF4, 0x19, 0xA1, 0x7F, 0x7A, 0xC3, 0x48, 0xFD, 0xD3,
0x83, 0xB1, 0xFA, 0x27, 0x06, 0x63, 0xF5, 0x4F, 0x0D, 0xC6, 0xEA, 0x9F, 0x61, 0xA4, 0xFE, 0x69,
0x1E, 0xAC, 0xD5, 0xBF, 0x39, 0x78, 0xAB, 0xFF, 0x76, 0xD0, 0x56, 0x7F, 0xED, 0xA0, 0xAD, 0xFE,
0xDE, 0x61, 0x5B, 0x7D, 0xBC, 0xC3, 0xB6, 0xFA, 0x7D, 0xA7, 0x6D, 0x75, 0xFA, 0x4E, 0xDB, 0xEA,
0x80, 0x8F, 0xB5, 0x2D, 0x00, 0x1F, 0x6B, 0x5B, 0x01, 0x3E, 0xD6, 0xB6, 0xF1, 0xBD, 0xB6, 0x55,
0xE3, 0x7B, 0x6D, 0xAB, 0xC2, 0xD7, 0xDA, 0xD6, 0x08, 0x98, 0x58, 0x5B, 0x06, 0x5C, 0xAC, 0xED,
};
const std::array<const unsigned char, 256> addr_0x41c3c0 = {
0x49, 0x13, 0x4D, 0x9B, 0x92, 0x26, 0x9A, 0x36, 0xA4, 0x89, 0xA6, 0xCD, 0x48, 0x9A, 0x68, 0xDA,
0x90, 0x34, 0xD1, 0xB4, 0x21, 0x69, 0xA2, 0x69, 0x43, 0xD2, 0x44, 0xD3, 0x24, 0x4D, 0x34, 0x6D,
0x86, 0xA4, 0x89, 0xA6, 0x0D, 0x49, 0x13, 0x4D, 0x1A, 0x92, 0x26, 0x9A, 0x6B, 0x48, 0x9A, 0x68,
0x35, 0x24, 0x4D, 0x34, 0xD7, 0x90, 0x34, 0xD1, 0xAE, 0x21, 0x69, 0xA2, 0xBA, 0x86, 0xA4, 0x89,
0x5D, 0x43, 0xD2, 0x44, 0x75, 0x0D, 0x49, 0x13, 0xEA, 0x1A, 0x92, 0x26, 0xD5, 0x35, 0x24, 0x4D,
0xAA, 0x6B, 0x48, 0x9A, 0x54, 0xD7, 0x90, 0x34, 0xA9, 0xAE, 0x21, 0x69, 0x52, 0x5D, 0x43, 0xD2,
0xA5, 0xBA, 0x86, 0xA4, 0x4B, 0x75, 0x0D, 0x49, 0x96, 0xEA, 0x1A, 0x92, 0x2C, 0xD5, 0x35, 0x24,
0x58, 0xAA, 0x6B, 0x48, 0xB1, 0x54, 0xD7, 0x90, 0x62, 0xA9, 0xAE, 0x21, 0xC4, 0x52, 0x5D, 0x43,
0x89, 0xA5, 0xBA, 0x86, 0x24, 0x96, 0xEA, 0x1A, 0x12, 0x4B, 0x75, 0x0D, 0x48, 0x2C, 0xD5, 0x35,
0x90, 0x58, 0xAA, 0x6B, 0x20, 0xB1, 0x54, 0xD7, 0x81, 0xC4, 0x52, 0x5D, 0x02, 0x89, 0xA5, 0xBA,
0x40, 0x62, 0xA9, 0xAE, 0x0A, 0x24, 0x96, 0xEA, 0x05, 0x12, 0x4B, 0x75, 0x2A, 0x90, 0x58, 0xAA,
0x55, 0x20, 0xB1, 0x54, 0xAA, 0x40, 0x62, 0xA9, 0x54, 0x81, 0xC4, 0x52, 0x15, 0x48, 0x2C, 0xD5,
0xA9, 0x02, 0x89, 0xA5, 0x53, 0x05, 0x12, 0x4B, 0xA7, 0x0A, 0x24, 0x96, 0x4E, 0x15, 0x48, 0x2C,
0x9D, 0x2A, 0x90, 0x58, 0x3A, 0x55, 0x20, 0xB1, 0x75, 0xAA, 0x40, 0x62, 0xEA, 0x54, 0x81, 0xC4,
0xAB, 0x4E, 0x15, 0x48, 0x56, 0x9D, 0x2A, 0x90, 0xAC, 0x3A, 0x55, 0x20, 0xD5, 0xA9, 0x02, 0x89,
0xAA, 0x53, 0x05, 0x12, 0x55, 0xA7, 0x0A, 0x24, 0xB3, 0xEA, 0x54, 0x81, 0x59, 0x75, 0xAA, 0x40,
};
const std::array<const unsigned char, 256> addr_0x41c4c0 = {
0xF5, 0xE7, 0x10, 0xAE, 0xB6, 0xFF, 0x87, 0x70, 0x6D, 0xFF, 0x0F, 0xE1, 0xDF, 0xDE, 0x1F, 0x42,
0xBF, 0xBD, 0x3F, 0x84, 0xEF, 0xEF, 0x21, 0xDC, 0xDB, 0xFF, 0x43, 0x38, 0x7B, 0x5B, 0x7F, 0x88,
0xF3, 0x96, 0xFE, 0x90, 0x82, 0x57, 0xF4, 0x07, 0x04, 0xAF, 0xE8, 0x0F, 0xE3, 0x0D, 0xFD, 0xA1,
0xC3, 0x3B, 0xFA, 0xC3, 0x4F, 0xF0, 0x8A, 0xFE, 0x9B, 0xC0, 0x15, 0x7D, 0x27, 0x78, 0x45, 0x7F,
0x09, 0x5E, 0xD1, 0x1F, 0x13, 0xBC, 0xA2, 0x3F, 0x36, 0x81, 0x2B, 0xFA, 0x68, 0x22, 0x57, 0x74,
0x45, 0x5A, 0xCA, 0x15, 0x93, 0x86, 0x72, 0xC5, 0xA5, 0xA9, 0x5C, 0x51, 0x4B, 0x53, 0xB9, 0xA2,
0x22, 0x2D, 0xE5, 0x0A, 0xD0, 0x44, 0xAE, 0xE8, 0x5F, 0x84, 0xA5, 0xDC, 0xBB, 0x28, 0x4B, 0x39,
0x77, 0x51, 0x96, 0x72, 0x8B, 0xB4, 0x94, 0x2B, 0x16, 0x69, 0x29, 0x57, 0x2D, 0xD2, 0x52, 0xAE,
0xEF, 0xA2, 0x2C, 0xE5, 0xDB, 0x65, 0x59, 0x4A, 0xB7, 0xCB, 0xB2, 0x94, 0x6A, 0xB7, 0x65, 0xA9,
0xA5, 0xBD, 0x96, 0x25, 0x4A, 0x7B, 0x2D, 0x4B, 0x95, 0xF6, 0x5A, 0x96, 0x2F, 0xCD, 0xB5, 0xAC,
0x5B, 0xBA, 0x6B, 0xD9, 0xB3, 0x54, 0xD7, 0x32, 0xD0, 0x4E, 0xCB, 0xD2, 0x67, 0xA9, 0xAE, 0x65,
0xCE, 0x52, 0x5D, 0xCB, 0x30, 0x0B, 0x75, 0x2D, 0x98, 0x85, 0xBA, 0x16, 0x60, 0x16, 0xEA, 0x5A,
0xC0, 0x2C, 0xD4, 0xB5, 0x0E, 0xD3, 0x50, 0x57, 0x1D, 0xA6, 0xA1, 0xAE, 0x3E, 0x6C, 0x43, 0xDD,
0x79, 0xF8, 0x86, 0x3A, 0xF2, 0xF0, 0x0D, 0x75, 0xE5, 0xE1, 0x1B, 0xEA, 0xCF, 0xE3, 0x37, 0x54,
0x85, 0x79, 0xA8, 0xEB, 0x74, 0x7E, 0xBF, 0x21, 0xE8, 0xFC, 0x7E, 0x43, 0x9E, 0xC7, 0x6F, 0xA8,
0x38, 0xAF, 0xDF, 0xD0, 0xD1, 0xF9, 0xFD, 0x86, 0xA7, 0xD3, 0xFB, 0x8D, 0x4A, 0x87, 0xF7, 0x9B
};
const std::array<const unsigned char, 256> addr_0x41c5c0 = {
0xDF, 0x8E, 0xCF, 0xDF, 0xFE, 0x76, 0x7C, 0xFE, 0xFC, 0xED, 0xF8, 0xFC, 0xF9, 0xDB, 0xF1, 0xF9,
0xF2, 0xB7, 0xE3, 0xF3, 0xBF, 0x1D, 0x9F, 0xBF, 0x7F, 0x3B, 0x3E, 0x7F, 0xE5, 0x6F, 0xC7, 0xE7,
0xCB, 0xDF, 0x8E, 0xCF, 0x5F, 0xFE, 0x76, 0x7C, 0xBE, 0xFC, 0xED, 0xF8, 0x97, 0xBF, 0x1D, 0x9F,
0x2F, 0x7F, 0x3B, 0x3E, 0xE0, 0xCB, 0xDF, 0x8E, 0xC1, 0x97, 0xBF, 0x1D, 0xF0, 0xE5, 0x6F, 0xC7,
0x7C, 0xF9, 0xDB, 0xF1, 0xF8, 0xF2, 0xB7, 0xE3, 0x82, 0x2F, 0x7F, 0x3B, 0x05, 0x5F, 0xFE, 0x76,
0x56, 0xC1, 0x97, 0xBF, 0x55, 0xF0, 0xE5, 0x6F, 0x15, 0x7C, 0xF9, 0xDB, 0x2A, 0xF8, 0xF2, 0xB7,
0xAB, 0xE0, 0xCB, 0xDF, 0x0A, 0xBE, 0xFC, 0xED, 0x61, 0x15, 0x7C, 0xF9, 0xC3, 0x2A, 0xF8, 0xF2,
0x86, 0x55, 0xF0, 0xE5, 0xAC, 0x82, 0x2F, 0x7F, 0x58, 0x05, 0x5F, 0xFE, 0xB0, 0x0A, 0xBE, 0xFC,
0x0C, 0xAB, 0xE0, 0xCB, 0x19, 0x56, 0xC1, 0x97, 0x32, 0xAC, 0x82, 0x2F, 0x65, 0x58, 0x05, 0x5F,
0x97, 0x61, 0x15, 0x7C, 0x2E, 0xC3, 0x2A, 0xF8, 0x5C, 0x86, 0x55, 0xF0, 0xB9, 0x0C, 0xAB, 0xE0,
0x73, 0x19, 0x56, 0xC1, 0xE7, 0x32, 0xAC, 0x82, 0xCB, 0xB0, 0x0A, 0xBE, 0xCE, 0x65, 0x58, 0x05,
0x9C, 0xCB, 0xB0, 0x0A, 0x72, 0x2E, 0xC3, 0x2A, 0x39, 0x97, 0x61, 0x15, 0xE4, 0x5C, 0x86, 0x55,
0xC8, 0xB9, 0x0C, 0xAB, 0x23, 0xE7, 0x32, 0xAC, 0x46, 0xCE, 0x65, 0x58, 0x8D, 0x9C, 0xCB, 0xB0,
0x1B, 0x39, 0x97, 0x61, 0x36, 0x72, 0x2E, 0xC3, 0x6C, 0xE4, 0x5C, 0x86, 0xD9, 0xC8, 0xB9, 0x0C,
0x91, 0x73, 0x19, 0x56, 0xCB, 0x46, 0xCE, 0x65, 0x96, 0x8D, 0x9C, 0xCB, 0xB2, 0x91, 0x73, 0x19,
0x65, 0x23, 0xE7, 0x32, 0x2C, 0x1B, 0x39, 0x97, 0x59, 0x36, 0x72, 0x2E, 0xB3, 0x6C, 0xE4, 0x5C
};
void fill_mat(mat_GF2& dst, unsigned long* t1, unsigned long* t2)
{
for (int i = 0; i < 64; ++i)
{
auto tmp = t1[i];
for (int k = 0; k < 32; ++k)
{
dst[k][i] = !!(tmp & 0x80000000);
tmp <<= 1;
}
tmp = t2[i];
for (int k = 32; k < 64; ++k)
{
dst[k][i] = !!(tmp & 0x80000000);
tmp <<= 1;
}
}
}
unsigned long long vec_2_int(vec_GF2& src, int from, int to)
{
unsigned long long ret = 0;
for (int i = from; i < to; ++i)
{
ret = (ret << 1) | (unsigned long long)to_int(rep(src[i]));
}
return ret;
}
int collapse(int argc, char** argv)
{
// key 是用户名经过 hash 计算得到的前三个，这里替换掉
unsigned int key[3] = { 0x83bb467a, 0x82023fba, 0xadd52abe };
unsigned int answer[3] = { 0,0,0 };
GF2 d;
vec_GF2 x, vec_key;
mat_GF2 m1, m2;
m1.SetDims(64, 64);
m2.SetDims(64, 64);
x.SetLength(64);
vec_key.SetLength(64);
fill_mat(m1, (unsigned long*)addr_0x41c4c0.data(), (unsigned long*)addr_0x41c5c0.data());
for (int i = 0; i < 32; ++i)
{
vec_key[i] = !!((key[1] << i) & 0x80000000);
vec_key[i + 32] = !!((key[2] << i) & 0x80000000);
}
solve(d, x, m1, vec_key); // 计算 x * A = b 中的 x， m1 = A，vec_key = b
answer[2] = vec_2_int(x, 32, 64, 31);
for (int i = 0; i < 32; ++i)
{
vec_key[i] = !!((key[0] << i) & 0x80000000);
vec_key[i + 32] = x[i];
}
fill_mat(m2, (unsigned long*)addr_0x41c2c0.data(), (unsigned long*)addr_0x41c3c0.data());
solve(d, x, m2, vec_key);
answer[1] = vec_2_int(x, 32, 64, 31);
answer[0] = vec_2_int(x, 0, 32, 31);
return 0;
}
有点没搞明白的是，当我把矩阵中的 bit 顺序换过来，即低位在前时计算结果会出错，完全变成了别的值，也不是正确结果的逆序，照理说应该都没什么差别才对……
