6. Bytes and Big Integers

Challenge 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

My Solution:

We can write a simply python script to replicate the results above of the hello string:

message = "HELLO"
ascii_bytes = []
hex_bytes = []
base_16 = ""
base_10 = 0

for i in message:
    ascii_bytes.append(ord(i))

for i in ascii_bytes:
    hex_bytes.append(hex(i))

base_16 += "0x"
for i in hex_bytes:
    base_16 += i.replace('0x', '')

base_10 = int(base_16.replace('0x', ''), 16)

print(message)
print(ascii_bytes)
print(hex_bytes)
print(base_16)
print(base_10)

And using the pycryptodome library we can solve this challenge:

from Crypto.Util.number import *

EncodedData = 11515195063862318899931685488813747395775516287289682636499965282714637259206269

print("Here is your flag:")
print(long_to_bytes(EncodedData).decode())

The Flag:

crypto{3nc0d1n6_4ll_7h3_********}