BASE64.md

Base64

The base64 encoding for CBC mode is the standard padded scheme. However, for EBC mode is a little unique.

The charset is also non standard: ./0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ

Encoding

8 bytes are encoded at a time, so inputs must be padded if not a multiple of 8.

Using an example input of: qwertyui

The hex and binary representations of the ascii characters are:

ascii	hex	binary
q	71	01110001
w	77	01110111
e	65	01100101
r	72	01110010
t	74	01110100
y	79	01111001
u	75	01110101
i	69	01101001

Taking the first 4 bytes (left), reading from the left and shifting to the left to form a 32 bit integer:

ascii	q	w	e	r
binary (8 bit)	01110001	01110111	01100101	01110010

The resulting 6 bit encoding with the charset is:

binary (6 bit)	01	110001	011101	110110	010101	110010
dec (index)	1	49	29	54	21	50
base64	/	L	r	Q	j	M

Similarly for the second 4 bytes (right):

ascii	t	y	u	i
binary (8 bit)	01110100	01111001	01110101	01101001

binary (6 bit)	01	110100	011110	010111	010101	101001
dec (index)	1	52	30	23	21	41
base64	/	O	s	l	j	D

The reading the right bytes first, from the right and shifting to the right results in the output: DjlsO/MjQrL/

Decoding

12 bytes are decoded at a time, so inputs must be padded if not a multiple of 12.

Now the reverse is shown with an input of: DjlsO/MjQrL/

The decimal (index into the charset) and binary representation of the ascii characters are:

ascii	index	binary (6 bits)
D	41	101001
j	21	010101
l	23	010111
s	30	011110
O	52	110100
/	1	000001
M	50	110010
j	21	010101
Q	54	110110
r	29	110010
L	49	110001
/	1	000001

Taking the first 6 bytes (right), reading from the right, looking up their index into the charset and shifting to the left to form a 32 bit integer:

base64	/	O	s	l	j	D
dec (index)	1	52	30	23	21	41
binary (6 bit)	000001	110100	011110	010111	010101	101001

Dropping 2 null bytes, the resulting 8 bit (ascii) encoding is:

binary (8 bit)	0000	01110100	01111001	01110101	01101001
hex		74	79	75	69
ascii		t	y	u	i

Similarly, for the second 6 bytes (left):

base64	/	L	r	Q	j	M
dec (index)	1	49	29	54	21	50
binary (6 bit)	000001	110001	011101	110110	010101	110010

binary (8 bit)	0000	01110001	01110111	01100101	01110010
hex		71	77	65	72
ascii		q	w	e	r

Then reading the left bytes first, from the left and shifting to the right results in the output: qwertyui