Base64 encoder and decoder
Interface

assert bytes(decode(encode(list('foo'.encode())))).decode() == 'foo'


To avoid using encode on strings or decode on bytes, you can use byte literals: b'foo'. This simplifies the writting to:

assert bytes(decode(encode(list(b'foo')))) == b'foo'


But then this let me wonder, why do the caller have to convert the arguments themselves? Why the need for list and bytes. A proper usage would be

assert decode(encode(b'foo')) == b'foo'


Which might let someone wonder decode to/encode from what? But assuming the module is properly named, that should not be an issue.

Now onto building functions that accept/returns bytes

Iteration and padding

When it comes to iterating over something in Python, it is deemed inelegant (and somewhat slower) to use indices rather than directly accessing content. Meaning for element in array: is way better than for i in range(len(array)): element = array[i]. Here you can argue that you can't easily iterate over groups of 3 or 4 elements at a time, but its forgetting about the itertools module and its variety of recipes.

grouper is the one you need:

from itertools import zip_longest


def grouper(iterable, n, fillvalue=0):
    "Collect data into fixed-length chunks or blocks"
    # grouper('ABCDEFG', 3, 'x') --&gt; ABC DEF Gxx"
    args = [iter(iterable)] * n
    return zip_longest(*args, fillvalue=fillvalue)


There is thus no need to manually handle the padding in encode and you can simplify iteration:

for first, second, third in grouper(unpadded_buf, 3):
    encoded_padded_buf += [ first &gt;&gt; 2 ]
    encoded_padded_buf += [ (first &amp; 3) &lt;&lt; 4 | second &gt;&gt; 4 ]
    encoded_padded_buf += [ (second &amp; 15) &lt;&lt; 2 | third &gt;&gt; 6 ]
    encoded_padded_buf += [ third &amp; 63]


It also has the advantage to handle any iterable the same way. Meaning you don't need to convert your bytes to list beforehand, it will do just fine.

Extra characters

You don't need to differentiate the case where len(unpadded_buf) % 3 is 1 or 2. You can perform the same task using:

extra = len(unpadded_buf) % 3
if extra:
    return asciied[-extra:] + '='*extra
return asciied


You can also note that there is no reason to make a copy of asciied, like you don't make a copy of decoded_buf in decode.

ALPHABET?

It feels like this variable is misnamed, it is not an alphabet, it is a convertion table TO_BASE64. Same for _alphabet, I would have named it FROM_BASE64 and computed it once, as a constant, as its content would never be different.

I would also incorporate {'=': 0} to simplify the map call.

So far, the code could be:

import string
from itertools import zip_longest


TO_BASE64 = dict(zip(range(64),
                     string.ascii_uppercase + string.ascii_lowercase +
                     string.digits + '+/'))
FROM_BASE64 = {v: k for k, v in TO_BASE64.items()}
FROM_BASE64['='] = 0


def grouper(iterable, n, fillvalue=0):
    "Collect data into fixed-length chunks or blocks"
    # grouper('ABCDEFG', 3, 'x') --&gt; ABC DEF Gxx"
    args = [iter(iterable)] * n
    return zip_longest(*args, fillvalue=fillvalue)


def encode(unpadded_buf):
    encoded_buf = []
    for first, second, third in grouper(unpadded_buf, 3):
        encoded_buf += [ first &gt;&gt; 2 ]
        encoded_buf += [ (first &amp; 3) &lt;&lt; 4 | second &gt;&gt; 4 ]
        encoded_buf += [ (second &amp; 15) &lt;&lt; 2 | third &gt;&gt; 6 ]
        encoded_buf += [ third &amp; 63]

    asciied = ''.join(TO_BASE64[n] for n in encoded_buf)
    extra = len(unpadded_buf) % 3
    if extra:
        return asciied[-extra:] + '='*extra

    return asciied


def decode(asciied):
    encoded_buf = (FROM_BASE64[n] for n in asciied)
    decoded_buf = []
    for first, second, third, fourth in grouper(encoded_buf, 4):
        decoded_buf += [ first &lt;&lt; 2 | second &gt;&gt; 4 ]
        decoded_buf += [ (second &amp; 15) &lt;&lt; 4 | third &gt;&gt; 2 ]
        decoded_buf += [ (third &amp; 3) &lt;&lt; 6 | fourth ]

    return bytes(decoded_buf)


if __name__ == '__main__':
    assert decode(encode(b'foo')) == b'foo'


Adding elements to a list

You extend your "result" lists using other lists. It is rather inefficient as the list you use to extend the first one will be discarded right away. You’d be better of appending values to the "result" instead. Or use helper generator functions to build results as they are computed without having to populate a list that will be discarded right after:

import string
from itertools import zip_longest


TO_BASE64 = dict(zip(range(64),
                     string.ascii_uppercase + string.ascii_lowercase +
                     string.digits + '+/'))
FROM_BASE64 = {v: k for k, v in TO_BASE64.items()}
FROM_BASE64['='] = 0


def grouper(iterable, n, fillvalue=0):
    "Collect data into fixed-length chunks or blocks"
    # grouper('ABCDEFG', 3, 'x') --&gt; ABC DEF Gxx"
    args = [iter(iterable)] * n
    return zip_longest(*args, fillvalue=fillvalue)


def _encoder(stream):
    for first, second, third in grouper(stream, 3):
        yield first &gt;&gt; 2
        yield (first &amp; 3) &lt;&lt; 4 | second &gt;&gt; 4
        yield (second &amp; 15) &lt;&lt; 2 | third &gt;&gt; 6
        yield third &amp; 63

def encode(unpadded_buf):
    asciied = ''.join(TO_BASE64[n] for n in _encoder(unpadded_buf))
    extra = len(unpadded_buf) % 3
    if extra:
        return asciied[-extra:] + '='*extra

    return asciied


def _decoder(stream):
    for first, second, third, fourth in grouper(stream, 4):
        yield first &lt;&lt; 2 | second &gt;&gt; 4
        yield (second &amp; 15) &lt;&lt; 4 | third &gt;&gt; 2
        yield (third &amp; 3) &lt;&lt; 6 | fourth

def decode(asciied):
    return bytes(_decoder(FROM_BASE64[n] for n in asciied))


if __name__ == '__main__':
    assert decode(encode(b'foo')) == b'foo'