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最新推荐文章于 2023-12-11 08:56:35 发布

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本文介绍了一种用于生成特定数学软件有效许可密钥的算法。该算法通过逆向工程和数学运算，从输入的MathID和预定义的密钥模板中生成符合要求的许可证密钥。涉及的主要步骤包括初始化哈希值、定义魔法数字、计算下一个哈希值以及生成最终的密钥。

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#include <stdint.h>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>

#define BUFFER_SIZE 64

// KEY: [0-9]{4}-[0-9]{4}-[0-9A-Z]{6}
#define KEY “1234-4321-123456”

/**

[LICENSE_TYPE]
Professional: 0 1 8 9
Trial: 2 3 6 7
Student: 4 5
CDF Player: 10 11
CDF Player Trial: 12 13
*/
#define LICENSE_TYPE “1”

/**

[INIT_HASH]
Mathematica 11.0.1: 0x25DB
Mathematica 11.1: 0x42DD 0x29C2
Mathematica 11.2: 0x6A91 0x29C2
Mathematica 11.3: 0xA439 0x29F8
Mathematica Other: 0xA68B 0xE4A8 0x2FDB 0xD227 0xDB75 0xEE71 0x44F1 0x0D00 0x72C4 0x8330 0x81DD 0x47C5 0xB4D3 0xAB0B 0x6188 0xBF47 0x1330 0xF536 0xA5CE 0x755E 0x1361
SystemModeler 5.0: 0x8330 0x81DD 0x47C5 0xB4D3 0xAB0B 0x6188 0xBF47 0x1330
SystemModeler 5.1.0: 0x81DD
To find the hash for future releases,
look up for 85 C0 7E 0E 39 3C 8D in WolframEngine.dll (32-bits),
get the following oprand (such as 0x11D9D790, MIND THE ENDIAN),
go to the address
(Do a conversion from VA to File Offset,

(virtual address found) + (offset of .text section) - (virtual address of .text section) - (image base) = (file offset).

Using Address Converter in CFF Explorer is recommended),

there are the accepted hash values (MIND THE ENDIAN as the same).
For who want to DIY, the easiest way to find password checking call is search for 0x105C3 and etc.
*/
#define INIT_HASH 0x29F8
#define HASH_MAGIC_1 0x105C3
#define HASH_MAGIC_2 0x1064B
#define GOOD_HASH 0xA5B6

static uint_fast8_t getDigit(uint_fast32_t number, uint_fast8_t digit){
return (uint_fast8_t) ((number / (uint_fast32_t)pow(10, digit - 1)) % 10);
}

// inverse of privHash: nextHash(privHash(x, y, c), c, y, c) == x
static uint_fast32_t nextHash(uint_fast32_t hash, uint_fast8_t byte, uint_fast32_t magic) {
for (uint_fast8_t bitIndex = 0; bitIndex <= 7; bitIndex++) {
uint_fast8_t bit = (byte >> bitIndex) & 1;
if (bit + ((hash - bit) & ~1) == hash) {
hash = (hash - bit) >> 1;
} else {
hash = ((magic - bit) ^ hash) >> 1;
}
}
return hash;
}

/*
static uint_fast32_t privHash(uint_fast32_t hash, uint_fast8_t byte, uint_fast32_t magic) {
for (uint_fast8_t bitIndex = 7; bitIndex >= 0; bitIndex–) {
uint_fast8_t bit = (byte >> bitIndex) & 1;
uint_fast32_t temp = (hash << 1) + bit;
if (hash & 0x8000) {
temp ^= magic;
}
hash = temp;
}
return hash;
}
*/

void genPass(char* string, uint_fast8_t length) {

uint_fast32_t hash = INIT_HASH;
for (int byteIndex = length - 1; byteIndex >= 0; byteIndex--) {
    hash = nextHash(hash, string[byteIndex], HASH_MAGIC_1);
}

uint_fast32_t n1 = 0;
while (nextHash(nextHash(hash, n1 & 0xFF, HASH_MAGIC_1), n1 >> 8, HASH_MAGIC_1) != GOOD_HASH) {
    if (++n1 >= 0xFFFF) {
        printf("Failed to find a key!");
        return;
    }
}

n1 = (uint_fast32_t) floor(((n1 + 0x72FA) & 0xFFFF) * 99999.0 / 0xFFFF);

uint_fast32_t temp = (n1/1000*1000) + n1%1000/100 + n1%100*10;
temp = (uint_fast32_t) ceil((temp / 99999.0) * 0xFFFF);
temp = nextHash(nextHash(0, temp & 0xFF, HASH_MAGIC_2), temp >> 8, HASH_MAGIC_2);

for (int byteIndex = length - 1; byteIndex >= 0; byteIndex--) {
    temp = nextHash(temp, (uint_fast8_t) string[byteIndex], HASH_MAGIC_2);
}

uint_fast16_t n2 = 0;
while (nextHash(nextHash(temp, n2 & 0xFF, HASH_MAGIC_2), n2 >> 8, HASH_MAGIC_2) != GOOD_HASH) {
    if (++n2 >= 0xFFFF) {
        printf("Failed to find a key!");
        return;
    }
}
n2 = (uint_fast16_t) floor((n2 & 0xFFFF) * 99999.0 / 0xFFFF);
printf("%u%u%u%u-%u%u%u-%u%u%u::1",
       getDigit(n2,2),getDigit(n1,2),getDigit(n1,4),getDigit(n1,5),
       getDigit(n2,1),getDigit(n1,3),getDigit(n2,5),
       getDigit(n2,3),getDigit(n1,1),getDigit(n2,4)
);

}

int main(){
char buffer[BUFFER_SIZE];
int offset = 0;
scanf("%s%n", buffer, &offset); // Input MathID here
strcpy(buffer+offset, “$” LICENSE_TYPE “&” KEY);
genPass(buffer, (uint_fast8_t) strlen(buffer));
return 0;
}