# Bytes and Big Integers

## Description

> Cryptosystems like RSA works on numbers, but messages are made up of characters. How should we convert our messages into numbers so that mathematical operations can be applied?\
> \
> The most common way is to take the ordinal bytes of the message, convert them into hexadecimal, and concatenate. This can be interpreted as a base-16/hexadecimal number, and also represented in base-10/decimal.\
> \
> To illustrate:<br>
>
> `message: HELLO`\
> `ascii bytes: [72, 69, 76, 76, 79]`\
> `hex bytes: [0x48, 0x45, 0x4c, 0x4c, 0x4f]`\
> `base-16: 0x48454c4c4f`\
> `base-10: 310400273487`\
> \
> :bulb: Python's PyCryptodome library implements this with the methods `bytes_to_long()` and `long_to_bytes()`. You will first have to install PyCryptodome and import it with `from Crypto.Util.number import *`. For more details check the [FAQ](https://cryptohack.org/faq/#install).\
> \
> Convert the following integer back into a message:\
> \
> `11515195063862318899931685488813747395775516287289682636499965282714637259206269`

## Byte the Long

We are given a long and we want bytes, so let us call `long_to_bytes`

```python
from Crypto.Util.number import *

# Integer, not a string!
LONG = 11515195063862318899931685488813747395775516287289682636499965282714637259206269

# Convert to bytes
bytes = long_to_bytes(LONG)

print(bytes)
```

## Flag

`crypto{3nc0d1n6_4ll_7h3_w4y_d0wn}`