Network Working Group S. Josefsson, Ed.
Request for Comments: 3548 July 2003
Category: Informational

The Base16, Base32, and Base64 Data Encodings

Status of this Memo

This memo provides information for the Internet community. It does
not specify an Internet standard of any kind. Distribution of this
memo is unlimited.

Copyright Notice

Copyright (C) The Internet Society (2003). All Rights Reserved.

Abstract

This document describes the commonly used base 64, base 32, and base
16 encoding schemes. It also discusses the use of line-feeds in
encoded data, use of padding in encoded data, use of non-alphabet
characters in encoded data, and use of different encoding alphabets.

Table of Contents

1. IntrodUCtion . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Implementation discrepancies . . . . . . . . . . . . . . . . . 2
2.1. Line feeds in encoded data . . . . . . . . . . . . . . . 2
2.2. Padding of encoded data . . . . . . . . . . . . . . . . 3
2.3. Interpretation of non-alphabet characters in encoded
data . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.4. Choosing the alphabet . . . . . . . . . . . . . . . . . 3
3. Base 64 Encoding . . . . . . . . . . . . . . . . . . . . . . . 4
4. Base 64 Encoding with URL and Filename Safe Alphabet . . . . . 6
5. Base 32 Encoding . . . . . . . . . . . . . . . . . . . . . . . 6
6. Base 16 Encoding . . . . . . . . . . . . . . . . . . . . . . . 8
7. Illustrations and examples . . . . . . . . . . . . . . . . . . 9
8. Security Considerations . . . . . . . . . . . . . . . . . . . 10
9. References . . . . . . . . . . . . . . . . . . . . . . . . . . 11
9.1. Normative References . . . . . . . . . . . . . . . . . . 11
9.2. Informative References . . . . . . . . . . . . . . . . . 11
10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 11
11. Editor's Address . . . . . . . . . . . . . . . . . . . . . . . 12
12. Full Copyright Statement . . . . . . . . . . . . . . . . . . . 13

1. Introduction

Base encoding of data is used in many situations to store or transfer
data in environments that, perhaps for legacy reasons, are restricted
to only US-ASCII [9] data. Base encoding can also be used in new
applications that do not have legacy restrictions, simply because it
makes it possible to manipulate objects with text editors.

In the past, different applications have had different requirements
and thus sometimes implemented base encodings in slightly different
ways. Today, protocol specifications sometimes use base encodings in
general, and "base64" in particular, without a precise description or
reference. MIME [3] is often used as a reference for base64 without
considering the consequences for line-wrapping or non-alphabet
characters. The purpose of this specification is to establish common
alphabet and encoding considerations. This will hopefully reduce
ambiguity in other documents, leading to better interoperability.

The key Words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC2119 [1].

2. Implementation discrepancies

Here we discuss the discrepancies between base encoding
implementations in the past, and where appropriate, mandate a
specific recommended behavior for the future.

2.1. Line feeds in encoded data

MIME [3] is often used as a reference for base 64 encoding. However,
MIME does not define "base 64" per se, but rather a "base 64
Content-Transfer-Encoding" for use within MIME. As such, MIME
enforces a limit on line length of base 64 encoded data to 76
characters. MIME inherits the encoding from PEM [2] stating it is
"virtually identical", however PEM uses a line length of 64
characters. The MIME and PEM limits are both due to limits within
SMTP.

Implementations MUST NOT not add line feeds to base encoded data
unless the specification referring to this document eXPlicitly
directs base encoders to add line feeds after a specific number of
characters.

2.2. Padding of encoded data

In some circumstances, the use of padding ("=") in base encoded data
is not required nor used. In the general case, when assumptions on
size of transported data cannot be made, padding is required to yield
correct decoded data.

Implementations MUST include appropriate pad characters at the end of
encoded data unless the specification referring to this document
explicitly states otherwise.

2.3. Interpretation of non-alphabet characters in encoded data

Base encodings use a specific, reduced, alphabet to encode binary
data. Non alphabet characters could exist within base encoded data,
caused by data corruption or by design. Non alphabet characters may
be exploited as a "covert channel", where non-protocol data can be
sent for nefarious purposes. Non alphabet characters might also be
sent in order to exploit implementation errors leading to, e.g.,
buffer overflow attacks.

Implementations MUST reject the encoding if it contains characters
outside the base alphabet when interpreting base encoded data, unless
the specification referring to this document explicitly states
otherwise. Such specifications may, as MIME does, instead state that
characters outside the base encoding alphabet should simply be
ignored when interpreting data ("be liberal in what you accept").
Note that this means that any CRLF constitute "non alphabet
characters" and are ignored. Furthermore, such specifications may
consider the pad character, "=", as not part of the base alphabet
until the end of the string. If more than the allowed number of pad
characters are found at the end of the string, e.g., a base 64 string
terminated with "===", the excess pad characters could be ignored.

2.4. Choosing the alphabet

Different applications have different requirements on the characters
in the alphabet. Here are a few requirements that determine which
alphabet should be used:

o Handled by humans. Characters "0", "O" are easily interchanged,
as well "1", "l" and "I". In the base32 alphabet below, where 0
(zero) and 1 (one) is not present, a decoder may interpret 0 as
O, and 1 as I or L depending on case. (However, by default it
should not, see previous section.)

o Encoded into structures that place other requirements. For base
16 and base 32, this determines the use of upper- or lowercase
alphabets. For base 64, the non-alphanumeric characters (in
particular "/") may be problematic in file names and URLs.

o Used as identifiers. Certain characters, notably "+" and "/" in
the base 64 alphabet, are treated as word-breaks by legacy text
search/index tools.

There is no universally accepted alphabet that fulfills all the
requirements. In this document, we document and name some currently
used alphabets.

3. Base 64 Encoding

The following description of base 64 is due to [2], [3], [4] and [5].

The Base 64 encoding is designed to represent arbitrary sequences of
octets in a form that requires case sensitivity but need not be
humanly readable.

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:

(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.

4. Base 64 Encoding with URL and Filename Safe Alphabet

The Base 64 encoding with an URL and filename safe alphabet has been
used in [8].

An alternative alphabet has been suggested that used "~" as the 63rd
character. Since the "~" character has special meaning in some file
system environments, the encoding described in this section is
recommended instead.

This encoding should not be regarded as the same as the "base64"
encoding, and should not be referred to as only "base64". Unless
made clear, "base64" refer to the base 64 in the previous section.

This encoding is technically identical to the previous one, except
for the 62:nd and 63:rd alphabet character, as indicated in table 2.

Table 2: The "URL and Filename safe" 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 - (minus)
12 M 29 d 46 u 63 _ (understrike)
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

5. Base 32 Encoding

The following description of base 32 is due to [7] (with
corrections).

The Base 32 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 base 32 alphabet.
When encoding a bit stream via the base 32 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 3: The Base 32 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 base 32
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.

6. Base 16 Encoding

The following description is original but analogous to previous
descriptions. Essentially, Base 16 encoding is the standard standard
case insensitive hex encoding, and may be referred to as "base16" or
"hex".

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 5: The Base 16 Alphabet

Value Encoding Value Encoding Value Encoding Value Encoding
0 0 4 4 8 8 12 C
1 1 5 5 9 9 13 D
2 2 6 6 10 A 14 E
3 3 7 7 11 B 15 F

Unlike base 32 and base 64, no special padding is necessary since a
full code word is always available.

7. Illustrations and examples

To translate between binary and a base encoding, the input is stored
in a structure and the output is extracted. The case for base 64 is
displayed in the following figure, borrowed from [4].

+--first octet--+-second octet--+--third octet--+
7 6 5 4 3 2 1 07 6 5 4 3 2 1 07 6 5 4 3 2 1 0
+-----------+---+-------+-------+---+-----------+
5 4 3 2 1 05 4 3 2 1 05 4 3 2 1 05 4 3 2 1 0
+--1.index--+--2.index--+--3.index--+--4.index--+

The case for base 32 is shown in the following figure, borrowed from
[6]. Each successive character in a base-32 value represents 5
successive bits of the underlying octet sequence. Thus, each group
of 8 characters represents a sequence of 5 octets (40 bits).

1 2 3
01234567 89012345 67890123 45678901 23456789
+--------+--------+--------+--------+--------+
< 1 >< 2 >< 3 ><.4 >< 5.>< 6 ><.7 >< 8 >
+--------+--------+--------+--------+--------+
<===> 8th character
<====> 7th character
<===> 6th character
<====> 5th character
<====> 4th character
<===> 3rd character
<====> 2nd character
<===> 1st character

The following example of Base64 data is from [4].

Input data: 0x14fb9c03d97e
Hex: 1 4 f b 9 c 0 3 d 9 7 e
8-bit: 00010100 11111011 10011100 00000011 11011001
11111110
6-bit: 000101 001111 101110 011100 000000 111101 100111
111110
Decimal: 5 15 46 28 0 61 37 62
Output: F P u c A 9 l +

Input data: 0x14fb9c03d9
Hex: 1 4 f b 9 c 0 3 d 9
8-bit: 00010100 11111011 10011100 00000011 11011001
pad with 00
6-bit: 000101 001111 101110 011100 000000 111101 100100
Decimal: 5 15 46 28 0 61 36
pad with =
Output: F P u c A 9 k =

Input data: 0x14fb9c03
Hex: 1 4 f b 9 c 0 3
8-bit: 00010100 11111011 10011100 00000011
pad with 0000
6-bit: 000101 001111 101110 011100 000000 110000
Decimal: 5 15 46 28 0 48
pad with = =
Output: F P u c A w = =

8. Security Considerations

When implementing Base encoding and decoding, care should be taken
not to introduce vulnerabilities to buffer overflow attacks, or other
attacks on the implementation. A decoder should not break on invalid
input including, e.g., embedded NUL characters (ASCII 0).

If non-alphabet characters are ignored, instead of causing rejection
of the entire encoding (as recommended), a covert channel that can be
used to "leak" information is made possible. The implications of
this should be understood in applications that do not follow the
recommended practice. Similarly, when the base 16 and base 32
alphabets are handled case insensitively, alteration of case can be
used to leak information.

Base encoding visually hides otherwise easily recognized information,
such as passwords, but does not provide any computational
confidentiality. This has been known to cause security incidents
when, e.g., a user reports details of a network protocol exchange

(perhaps to illustrate some other problem) and accidentally reveals
the password because she is unaware that the base encoding does not
protect the password.

9. References

9.1. Normative References

[1] Bradner, S., "Key words for use in RFCs to Indicate Requirement
Levels", BCP 14, RFC2119, March 1997.

9.2. Informative References

[2] Linn, J., "Privacy Enhancement for Internet Electronic Mail:
Part I: Message Encryption and Authentication Procedures", RFC
1421, February 1993.

[3] Freed, N. and N. Borenstein, "Multipurpose Internet Mail
Extensions (MIME) Part One: Format of Internet Message Bodies",
RFC2045, November 1996.

[4] Callas, J., Donnerhacke, L., Finney, H. and R. Thayer, "OpenPGP
Message Format", RFC2440, November 1998.

[5] Eastlake, D., "Domain Name System Security Extensions", RFC2535,
March 1999.

[6] Klyne, G. and L. Masinter, "Identifying Composite Media
Features", RFC2938, September 2000.

[7] Myers, J., "SASL GSSAPI mechanisms", Work in Progress.

[8] Wilcox-O'Hearn, B., "Post to P2P-hackers mailing list", World
Wide Web http://zgp.org/pipermail/p2p-hackers/2001-
September/000315.Html, September 2001.

[9] Cerf, V., "ASCII format for Network Interchange", RFC20, October
1969.

10. Acknowledgements

Several people offered comments and suggestions, including Tony
Hansen, Gordon Mohr, John Myers, Chris Newman, and Andrew Sieber.
Text used in this document is based on earlier RFCs describing
specific uses of various base encodings. The author acknowledges the
RSA Laboratories for supporting the work that led to this document.

11. Editor's Address

Simon Josefsson
EMail: simon@josefsson.org

12. Full Copyright Statement

Copyright (C) The Internet Society (2003). All Rights Reserved.

This document and translations of it may be copied and furnished to
others, and derivative works that comment on or otherwise explain it
or assist in its implementation may be prepared, copied, published
and distributed, in whole or in part, without restriction of any
kind, provided that the above copyright notice and this paragraph are
included on all such copies and derivative works. However, this
document itself may not be modified in any way, such as by removing
the copyright notice or references to the Internet Society or other
Internet organizations, except as needed for the purpose of
developing Internet standards in which case the procedures for
copyrights defined in the Internet Standards process must be
followed, or as required to translate it into languages other than
English.

The limited permissions granted above are perpetual and will not be
revoked by the Internet Society or its successors or assignees.

This document and the information contained herein is provided on an
"AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.

Acknowledgement

Funding for the RFCEditor function is currently provided by the
Internet Society.