# Whose Base Is It Anyway

## Problem

Someone gave this ciphertext but I'm not sure how to solve it or what they based it off of. Seems tricky but can you figure it out?

## Solution

From first glance, we can see that the cipher is full of `A`s and `B`s. This is binary, i.e. base 2. After we decode this, we will get another string with `A`s, `B`s, `C`s and `D`s. This would be base 4.
This continues until base 64, where we are finally able to obtain our flag (base 64 decode).
Note that for base 32, we are using a custom alphabet.
Base 64 decode the obtained string:
Script:
from Crypto.Util.number import long_to_bytes
import base64
cipher = "    @                @            A    @                @        @    @    @        @        @            A    @            @    @        @        @                @                @        @        @        @    @    @                @        @    A    @            A    @        @    @    @                @            A    @        @    @    @        @    @    @                @        @    A    @            @    @        @    A    @                @            A    @            @    @        @    @    @        @        @            A    @            @    @        @        @                @            A    @                @        @    @    @        @        @            A    @            @    @        @        @                @            @    @        @        @        @    @    @                @        @    A    @            A    @            @    @                @            A    @                @        @    @    @        @        @        @    A    @            @    @        @    A    @                @                @        @        @        @    @    @                @        @    A    @            @    @        @        @                @            A    @                @        @    A    @            @    @            A    @            @    @        @        @                @            A    @                @        @    @    @                @        @    A    @            @    @        @    @    @                @            A    @        @    @    @        @    @    @        @    A    @            A    @            @    @        @    A    @                @        @    @    @            @    @        @    @    @                @        @    A    @            A    @        A        @                @            A    @        @        @        @    @    @                @            A    @            @    @        @    A    @                @                @            @    @        @    @    @                @        @    A    @            A    @                @                @            A    @        @    @    @        @    @    @            A    @        @    A    @            @    @        @        @                @            @    @        @        @        @    @    @        @        @            A    @            A    @        @        @                @            A    @                @        @    @    @        @    @    @            A    @            @    @        @    A    @                @        @        @        @        @        @    @    @                @        @    A    @            A    @                @                @            A    @        @    @    @        @    @    @        @        @            A    @            @    @        @        @                @            @    @        @    @    @        @    @    @        @        @            A    @            @    @        @    A    @                @            A    @        @    @    @        @    @    @                @        @    A    @            @    @        @    A    @                @                @            @    @        @    @    @                @        @    A    @            A    @        @        @                @            A    @                @        @    @    @        @    A    @        @    A    @            @    @        @    A    @                @        @        @        @    @    @        @    @    @                @        @    A    @            A    @            @    @                @            A    @        @    @    @        @    @    @        @    A    @            A    @            @    @        @        @                @                @        @        @        @    @    @        @        @            A    @            @    @        @    @    @                @            A    @        @    @    @        @    @    @        @    A    @        @    A    @            @    @        @    A    @                @        @        @        @        @        @    @    @                @        @    A    @            A    @        A        @                @            A    @                @        @    @    @            A    @            A    @            @    @        @        @                @            A    @                @        @    @    @                @        @    A    @            @    @        @    @    @                @            A    @        @    @    @        @    @    @                @        @    A    @            @    @        @    A    @                @        @        @                @        @    @    @        @        @        @    A    @            @    @                @                @            A    @                @        @    @    @        @        @            A    @            @    @        @        @                @                @        @    @    @        @    @    @        @        @        @    A    @            @    @        @    @    @                @            A    @        @    @    @        @    @    @            A    @            @"
def converter(figures, base):
#invert oder of figures (lowest count first)
figures = figures[::-1]
result = 0
#loop over all figures
for i in range(len(figures)):
#add the contirbution of the i-th figure
result += figures[i]*base**i
return result
curr_base = 2
print(cipher)
done = False
while not done:
figures = []
for char in cipher:
if char.islower() :
figures.append(26 + ord(char) - ord('a'))
elif ord(char) >= ord('A'):
diff = ord(char) - ord('A')
figures.append(diff)
while len(figures) % 8:
figures.append(0)
converted = converter(figures, curr_base)
result = long_to_bytes(converted)
# print(result)
cipher = result.decode()
print(curr_base)
print(cipher)
curr_base *= 2
if curr_base == 64:
break