
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

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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 RFC 2119 [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.

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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.)

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   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.

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                   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.

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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.

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   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,

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   (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.

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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 0|7 6 5 4 3 2 1 0|7 6 5 4 3 2 1 0|
         +-----------+---+-------+-------+---+-----------+
         |5 4 3 2 1 0|5 4 3 2 1 0|5 4 3 2 1 0|5 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

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   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

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   (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, RFC 2119, 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",
       RFC 2045, November 1996.

   [4] Callas, J., Donnerhacke, L., Finney, H. and R. Thayer, "OpenPGP
       Message Format", RFC 2440, November 1998.

   [5] Eastlake, D., "Domain Name System Security Extensions", RFC 2535,
       March 1999.

   [6] Klyne, G. and L. Masinter, "Identifying Composite Media
       Features", RFC 2938, 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", RFC 20, 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.

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11.  Editor's Address

   Simon Josefsson
   EMail: simon@josefsson.org

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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 RFC Editor function is currently provided by the
   Internet Society.

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