Converting an Integer value to base64, and then decoding it to get a plaintext

Question

I am given this number 427021005928, which i am supposed to change into a base64 encoded string and then decode the base64 string to get a plain text.

This decimal value 427021005928 when converted to binary gives 110001101101100011011110111010001101000 which corresponds to 'Y2xvdGg=', which is what i want. Got the conversion from (https://cryptii.com/pipes/binary-to-base64)

And then finally i decode 'Y2xvdGg=' to get the text cloth.

My problem is i do not have any idea how to use Python to get from either the decimal or binary value to get 'Y2xvdGg='

Some help would be appreciated!

NOTE: I only have this value 427021005928 at the start. I need to get the base64 and plaintext answers.

Answer 1

One elegant way would be using [Python 3]: struct - Interpret bytes as packed binary data, but given the fact that Python numbers are not fixed size, some additional computation would be required (for example, the number is 5 bytes long).

Apparently, the online converter, applied the base64 encoding on the number's memory representation, which can be obtained via [Python 3]: int.to_bytes(length, byteorder, *, signed=False)(endianness is important, and in this case it's big):

For the backwards process, reversed steps are required. There are 2 alternatives:

• Things being done manually (this could also be applied to the "forward" process)
• Using int.from_bytes

>>> import base64
>>>
>>> number = 427021005928
>>>
>>> number_bytes = number.to_bytes((number.bit_length() + 7) // 8, byteorder="big")  # Here's where the magic happens
>>> number_bytes, number_bytes.decode()
(b'cloth', 'cloth')
>>>
>>> encoded = base64.b64encode(number_bytes)
>>> encoded, encoded.decode()  # Don't let yourself tricked by the variable and method names resemblance
(b'Y2xvdGg=', 'Y2xvdGg=')
>>>
>>> # Now, getting the number back
...
>>> decoded = base64.b64decode(encoded)
>>> decoded
b'cloth'
>>>
>>> final_number0 = sum((item * 256 ** idx for idx, item in enumerate(reversed(decoded))))
>>> final_number0
427021005928
>>> number == final_number0
True
>>>
>>> # OR using from_bytes
...
>>> final_number1 = int.from_bytes(decoded, byteorder="big")
>>> final_number1
427021005928
>>> final_number1 == number
True

For more details on bitwise operations, check [SO]: Output of crc32b in PHP is not equal to Python (@CristiFati's answer).

Answer 2

Try this (https://docs.python.org/3/library/stdtypes.html#int.to_bytes)

>>> import base64
>>> x=427021005928
>>> y=x.to_bytes(5,byteorder='big').decode('utf-8')
>>> base64.b64encode(y.encode()).decode()
'Y2xvdGg='
>>> y
'cloth'