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:

message: HELLO ascii bytes: [72, 69, 76, 76, 79] hex bytes: [0x48, 0x45, 0x4c, 0x4c, 0x4f] base-16: 0x48454c4c4f base-10: 310400273487 💡 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. 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

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}