Network Working Group S.A. Josefsson (editor)
Internet-Draft Extundo
Expires: February 20, 2001 August 22, 2000
Base 64, 32 and 16 Encodings
draft-josefsson-base-encoding-00.txt
Status of this Memo
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Copyright Notice
Copyright (C) The Internet Society (2000). All Rights Reserved.
Abstract
This draft serve as a canonical collection of base 16, base 32 and
base 64 encoding descriptions.
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Table of Contents
1. Base 64 Encoding . . . . . . . . . . . . . . . . . . . . . . . 3
2. Base 32 Encoding . . . . . . . . . . . . . . . . . . . . . . . 5
3. Base 16 Encoding . . . . . . . . . . . . . . . . . . . . . . . 7
4. Security Considerations . . . . . . . . . . . . . . . . . . . 8
References . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Author's Address . . . . . . . . . . . . . . . . . . . . . . . 9
Full Copyright Statement . . . . . . . . . . . . . . . . . . . 10
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1. Base 64 Encoding
The following description of base64 is due to [1] and [2].
A 65-character subset of US-ASCII is used, enabling 6 bits to be
represented per printable character. (The extra 65th character, "=",
is used to signify a special processing function.)
The encoding process represents 24-bit groups of input bits as
output strings of 4 encoded characters. Proceeding from left to
right, a 24-bit input group is formed by concatenating 3 8-bit input
groups. These 24 bits are then treated as 4 concatenated 6-bit
groups, each of which is translated into a single digit in the base
64 alphabet.
Each 6-bit group is used as an index into an array of 64 printable
characters. The character referenced by the index is placed in the
output string.
Table 1: The Base 64 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
Special processing is performed if fewer than 24 bits are available
at the end of the data being encoded. A full encoding quantum is
always completed at the end of a quantity. When fewer than 24 input
bits are available in an input group, zero bits are added (on the
right) to form an integral number of 6-bit groups. Padding at the
end of the data is performed using the '=' character. Since all
base 64 input is an integral number of octets, only the following
cases can arise:
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(1) the final quantum of encoding input is an integral multiple of
24 bits; here, the final unit of encoded output will be an integral
multiple of 4 characters with no "=" padding,
(2) the final quantum of encoding input is exactly 8 bits; here, the
final unit of encoded output will be two characters followed by two
"=" padding characters, or
(3) the final quantum of encoding input is exactly 16 bits; here,
the final unit of encoded output will be three characters followed
by one "=" padding character.
Any characters outside of the base64 alphabet are to be ignored in
base64-encoded data.
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2. Base 32 Encoding
The following description of base32 is due to [3], the padding
section was updated to fix two typos.
The Base32 encoding is designed to represent arbitrary sequences of
octets in a form that needs to be case insensitive but need not be
humanly readable.
A 33-character subset of US-ASCII is used, enabling 5 bits to be
represented per printable character. (The extra 33rd character, "=",
is used to signify a special processing function.)
The encoding process represents 40-bit groups of input bits as
output strings of 8 encoded characters. Proceeding from left to
right, a 40-bit input group is formed by concatenating 5 8bit input
groups. These 40 bits are then treated as 8 concatenated 5-bit
groups, each of which is translated into a single digit in the
base32 alphabet. When encoding a bit stream via the base32
encoding, the bit stream must be presumed to be ordered with the
most-significant-bit first. That is, the first bit in the stream
will be the high-order bit in the first 8bit byte, and the eighth
bit will be the low-order bit in the first 8bit byte, and so on.
Each 5-bit group is used as an index into an array of 32 printable
characters. The character referenced by the index is placed in the
output string. These characters, identified in Table 2, below, are
selected from US-ASCII digits and uppercase letters.
Table 2: The Base32 Alphabet
Value Encoding Value Encoding Value Encoding Value Encoding
0 A 9 J 18 S 27 3
1 B 10 K 19 T 28 4
2 C 11 L 20 U 29 5
3 D 12 M 21 V 30 6
4 E 13 N 22 W 31 7
5 F 14 O 23 X
6 G 15 P 24 Y (pad) =
7 H 16 Q 25 Z
8 I 17 R 26 2
Special processing is performed if fewer than 40 bits are available
at the end of the data being encoded. A full encoding quantum is
always completed at the end of a body. When fewer than 40 input bits
are available in an input group, zero bits are added (on the right)
to form an integral number of 5-bit groups. Padding at the end of
the data is performed using the "=" character. Since all base32
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input is an integral number of octets, only the following cases can
arise:
(1) the final quantum of encoding input is an integral multiple of
40 bits; here, the final unit of encoded output will be an integral
multiple of 8 characters with no "=" padding,
(2) the final quantum of encoding input is exactly 8 bits; here, the
final unit of encoded output will be two characters followed by six
"=" padding characters,
(3) the final quantum of encoding input is exactly 16 bits; here,
the final unit of encoded output will be four characters followed by
four "=" padding characters,
(4) the final quantum of encoding input is exactly 24 bits; here,
the final unit of encoded output will be five characters followed by
three "=" padding characters, or
(5) the final quantum of encoding input is exactly 32 bits; here,
the final unit of encoded output will be seven characters followed
by one "=" padding character.
Because it is used only for padding at the end of the data, the
occurrence of any "=" characters may be taken as evidence that the
end of the data has been reached (without truncation in transit).
No such assurance is possible, however, when the number of octets
transmitted was a multiple of three and no "=" characters are
present.
Any characters outside of the base32 alphabet are to be ignored in
base32-encoded data.
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3. Base 16 Encoding
The following description is original but analog to previous
descriptions.
A 16-character subset of US-ASCII is used, enabling 4 bits to be
represented per printable character.
The encoding process represents 8-bit groups (octets) of input bits
as output strings of 2 encoded characters. Proceeding from left to
right, a 8-bit input is taken from the input data. These 8 bits are
then treated as 2 concatenated 4-bit groups, each of which is
translated into a single digit in the base 16 alphabet.
Each 4-bit group is used as an index into an array of 16 printable
characters. The character referenced by the index is placed in the
output string.
Table 3: The Base 16 Alphabet
Value Encoding Value Encoding Value Encoding Value Encoding
0 A 5 F 10 K 15 P
1 B 6 G 11 L 16 Q
2 C 7 H 12 M
3 D 8 I 13 N
4 E 9 J 14 O
Unlike base32 and base64, no special padding is necessery since a
full code words are always available.
Any characters outside of the base32 alphabet are to be ignored in
base32-encoded data.
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4. Security Considerations
This draft does not discuss security.
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References
[1] Freed, N. and N. Borenstein, "Multipurpose Internet Mail
Extensions (MIME) Part One: Format of Internet Message Bodies",
November 1996.
[2] Eastlake, D., "Domain Name System Security Extensions", March
1999.
[3] Myers, J., "SASL GSSAPI mechanisms", May 2000.
Author's Address
Simon Josefsson
Extundo
Drottningholmsvägen 70
Stockholm 112 42
Sweden
Phone: +46 8 6190422
EMail: simon@josefsson.org
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Acknowledgement
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