Decoding a Base64 encoded string

It is often necessary for some web servers to be able to authenticate users to allow access to a directory of file. There are many ways of doing this...one of the more common (and least secure) is Basic Authentication. Basic authentication uses Base64 to encode the user's name and password so there are no "clear" text passwords flying around the net as you get during ftp logins.

When viewed through a network sniffer auser name of "Administrator" and a password of "pass" appears as "QWRtaW5pc3RyYXRvcjpwYXNz". When the userID and password are encoded a colon (:) is used to seperate them. So :

"QWRtaW5pc3RyYXRvcjpwYXNz"
translates to
Administrator:pass
Base64 uses a 65 character subset of US-ASCII, allowing 6 bits for each character so the character "m" with a Base64 value of 38, when represented in binary form, is 100110.

When a text string, let's say "mne" is encoded this is what happens : The text string is converted into its US-ASCII value. (In US-ASCII each character is assigned a value) :

The character "m" has the decimal value of 109
The character "n" has the decimal value of 110
The character "e" has the decimal value of 101
so "mne" (a 3 8-bit-byte text string) is 109 110 101 in decimal form. When converted to binary the string looks like this :

01101101 01101110 01100101

These three 8-bit-bytes are concatenated (linked together) to make a 24 bit stream :

011011010110111001100101

This 24 bit stream is then split up into 4 6-bit sections :

011011 010110 111001 100101

We now have 4 values. These binary values, when converted into decimal form look like this:

27 22 57 37

Now each character of the Base64 character set has a decimal value. We now change these decimal values into the Base64 equivalent :

27 = b

22 = w

57 = 5

37 = l

So "mne" when encoded as Base64 reads as "bw5l". Below is a table of the Base64 character set with their decimal values :

                            Table 1: The Base64 Alphabet

      Value Encoding  Value Encoding  Value Encoding  Value Encoding
           0 A            17 R            34 i            51 z
           1 B            18 S            35 j            52 0
           2 C            19 T            36 k            53 1
           3 D            20 U            37 l            54 2
           4 E            21 V            38 m            55 3
           5 F            22 W            39 n            56 4
           6 G            23 X            40 o            57 5
           7 H            24 Y            41 p            58 6
           8 I            25 Z            42 q            59 7
           9 J            26 a            43 r            60 8
          10 K            27 b            44 s            61 9
          11 L            28 c            45 t            62 +
          12 M            29 d            46 u            63 /
          13 N            30 e            47 v
          14 O            31 f            48 w         (pad) =
          15 P            32 g            49 x
          16 Q            33 h            50 y

When decoding a Base64 string just do the reverse :

1)Convert the character to it's Base64 decimal value.

2)Convert this decimal value into binary.

3)Squash the 6 bits of each character into one big string of binary digits.

4)Split this string up into groups of 8 bits (starting from right to left).

5)Convert each 8-bit binary value into a decimal number.

6)Convert this decimal value into its US-ASCII equivalent.

And thats all there is to decoding a Base64 encoded string :o)