The Base45 Data Encoding
draft-faltstrom-base45-12

Network Working Group                                       P. Faltstrom
Internet-Draft                                                    Netnod
Intended status: Informational                              F. Ljunggren
Expires: December 18, 2022                                         Kirei
                                                            D. van Gulik
                                                              Webweaving
                                                           June 16, 2022

                        The Base45 Data Encoding
                       draft-faltstrom-base45-12

Abstract

   This document describes the Base45 encoding scheme which is built
   upon the Base64, Base32 and Base16 encoding schemes.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Conventions Used in This Document . . . . . . . . . . . . . .   2
   3.  Interpretation of Encoded Data  . . . . . . . . . . . . . . .   2
   4.  The Base45 Encoding . . . . . . . . . . . . . . . . . . . . .   3
     4.1.  When to, and not to, use Base45 . . . . . . . . . . . . .   4
     4.2.  The alphabet used in Base45 . . . . . . . . . . . . . . .   4
     4.3.  Encoding examples . . . . . . . . . . . . . . . . . . . .   4
     4.4.  Decoding examples . . . . . . . . . . . . . . . . . . . .   5
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   5
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   5
   7.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   6
   8.  Normative References  . . . . . . . . . . . . . . . . . . . .   6
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   7

1.  Introduction

   A QR-code is used to encode text as a graphical image.  Depending on
   the characters used in the text various encoding options for a QR-
   code exist, e.g.  Numeric, Alphanumeric and Byte mode.  Even in Byte
   mode a typical QR-code reader tries to interpret a byte sequence as a
   UTF-8 or ISO/IEC 8859-1 encoded text.  Thus, QR-codes cannot be used
   to encode arbitrary binary data directly.  Such data has to be
   converted into an appropriate text before that text could be encoded
   as a QR-code.  Compared to already established Base64, Base32 and
   Base16 encoding schemes, that are described in RFC 4648 [RFC4648],
   the Base45 scheme described in this document offer a more compact QR-
   code encoding.

   One important difference from those others and Base45 is the key
   table and that the padding with '=' is not required.

2.  Conventions Used in This Document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Interpretation of Encoded Data

   Encoded data is to be interpreted as described in RFC 4648 [RFC4648]
   with the exception that a different alphabet is selected.

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4.  The Base45 Encoding

   QR codes have a limited ability to store binary data.  In practice
   binary data have to be encoded in characters according to one of the
   modes already defined in the standard for QR codes.  The easiest mode
   to use in called Alphanumeric mode (see section 7.3.4 and Table 2 of
   ISO/IEC 18004:2015 [ISO18004]).  Unfortunately Alphanumeric mode uses
   45 different characters which implies neither Base32 nor Base64 are
   very effective encodings.

   A 45-character subset of US-ASCII is used; the 45 characters usable
   in a QR code in Alphanumeric mode (see section 7.3.4 and Table 2 of
   ISO/IEC 18004:2015 [ISO18004]).  Base45 encodes 2 bytes in 3
   characters, compared to Base64, which encodes 3 bytes in 4
   characters.

   For encoding, two bytes [a, b] MUST be interpreted as a number n in
   base 256, i.e. as an unsigned integer over 16 bits so that the number
   n = (a*256) + b.

   This number n is converted to base 45 [c, d, e] so that n = c +
   (d*45) + (e*45*45).  Note the order of c, d and e which are chosen so
   that the left-most [c] is the least significant.

   The values c, d and e are then looked up in Table 1 to produce a
   three character string.  The process is reversed when decoding.

   For encoding a single byte [a], it MUST be interpreted as a base 256
   number, i.e. as an unsigned integer over 8 bits.  That integer MUST
   be converted to base 45 [c d] so that a = c + (45*d).  The values c
   and d are then looked up in Table 1 to produce a two character
   string.

   A byte string [a b c d ... x y z] with arbitrary content and
   arbitrary length MUST be encoded as follows: From left to right pairs
   of bytes MUST be encoded as described above.  If the number of bytes
   is even, then the encoded form is a string with a length which is
   evenly divisible by 3.  If the number of bytes is odd, then the last
   (rightmost) byte MUST be encoded on two characters as described
   above.

   For decoding a Base45 encoded string the inverse operations are
   performed.

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4.1.  When to, and not to, use Base45

   If binary data is to be stored in a QR-Code, the suggested mechanism
   is to use the Alphanumeric mode that uses 11 bits for 2 characters as
   defined in section 7.3.4 in ISO/IEC 18004:2015 [ISO18004].  The ECI
   mode indicator for this encoding is 0010.

   On the other hand if the data is to be sent via some other transport,
   a transport encoding suitable for that transport should be used
   instead of Base45.  For example, it is not recommended to first
   encode data in Base45 and then encode the resulting string in Base64
   if the data is to be sent via email.  Instead, the Base45 encoding
   should be removed, and the data itself should be encoded in Base64.

4.2.  The alphabet used in Base45

   The Alphanumeric mode is defined to use 45 characters as specified in
   this alphabet.

                  Table 1: The Base45 Alphabet

   Value Encoding  Value Encoding  Value Encoding  Value Encoding
      00 0            12 C            24 O            36 Space
      01 1            13 D            25 P            37 $
      02 2            14 E            26 Q            38 %
      03 3            15 F            27 R            39 *
      04 4            16 G            28 S            40 +
      05 5            17 H            29 T            41 -
      06 6            18 I            30 U            42 .
      07 7            19 J            31 V            43 /
      08 8            20 K            32 W            44 :
      09 9            21 L            33 X
      10 A            22 M            34 Y
      11 B            23 N            35 Z

4.3.  Encoding examples

   It should be noted that although the examples are all text, Base45 is
   an encoding for binary data where each octet can have any value
   0-255.

   Encoding example 1: The string "AB" is the byte sequence [65 66].
   The 16 bit value is 65 * 256 + 66 = 16706. 16706 equals 11 + 45 * 11
   + 45 * 45 * 8, so the sequence in base 45 is [11 11 8].  By looking
   up these values in the Table 1 we get the encoded string "BB8".

   Encoding example 2: The string "Hello!!" as ASCII is the byte
   sequence [72 101 108 108 111 33 33].  If we look at each 16 bit

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   value, it is [18533 27756 28449 33].  Note the 33 for the last byte.
   When looking at the values in base 45, we get [[38 6 9] [36 31 13] [9
   2 14] [33 0]] where the last byte is represented by two.  The
   resulting string "%69 VD92EX0" is created by looking up these values
   in Table 1.  It should be noted it includes a space.

   Encoding example 3: The string "base-45" as ASCII is the byte
   sequence [98 97 115 101 45 52 53].  If we look at each 16 bit value,
   it is [25185 29541 11572 53].  Note the 53 for the last byte.  When
   looking at the values in base 45, we get [[30 19 12] [21 26 14] [7 32
   5] [8 1]] where the last byte is represented by two.  By looking up
   these values in the Table 1 we get the encoded string "UJCLQE7W581".

4.4.  Decoding examples

   Decoding example 1: The string "QED8WEX0" represents, when looked up
   in Table 1, the values [26 14 13 8 32 14 33 0].  We arrange the
   numbers in chunks of three, except for the last one which can be two,
   and get [[26 14 13] [8 32 14] [33 0]].  In base 45 we get [26981
   29798 33] where the bytes are [[105 101] [116 102] [33]].  If we look
   at the ASCII values we get the string "ietf!".

5.  IANA Considerations

   There are no considerations for IANA in this document.

6.  Security Considerations

   When implementing encoding and decoding it is important to be very
   careful so that buffer overflow or similar does not occur.  This of
   course includes the calculations in base 45 and lookup in the table
   of characters (Table 1).  A decoder must also be robust regarding
   input, including proper handling of any octet value 0-255, including
   the NUL character (ASCII 0).

   It should be noted that Base64 and some other encodings pad the
   string so that the encoding starts with an aligned number of
   characters while Base45 specifically avoids padding.  Because of
   this, special care has to be taken when odd number of octets are to
   be encoded.  Similarly, care must be taken if the number of
   characters to decode are not evenly divisible by 3.

   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

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   sent in order to exploit implementation errors leading to, e.g.,
   buffer overflow attacks.

   Implementations MUST reject any input that is not a valid encoding.
   For example, it MUST reject the input (encoded data) if it contains
   characters outside the base alphabet (in Table 1) when interpreting
   base-encoded data.

   Even though a Base45 encoded string contains only characters from the
   alphabet in Table 1, cases like the following has to be considered:
   The string "FGW" represents 65535 (FFFF in base 16), which is a valid
   encoding of 16 bits.  A slightly different encoded string of the same
   length, "GGW", would represent 65536 (10000 in base 16), which is
   represented by more than 16 bits.  Implementations MUST also reject
   the encoded data if it contains a triplet of characters which, when
   decoded, results in an unsigned integer which is greater than 65535
   (ffff in base 16).

   It should be noted that the resulting string after encoding to Base45
   might include non-URL-safe characters so if the URL including the
   Base45 encoded data has to be URL safe, one has to use %-encoding.

7.  Acknowledgements

   The authors thank Mark Adler, Anders Ahl, Alan Barrett, Sam Spens
   Clason, Alfred Fiedler, Tomas Harreveld, Erik Hellman, Joakim
   Jardenberg, Michael Joost, Erik Kline, Christian Landgren, Anders
   Lowinger, Mans Nilsson, Jakob Schlyter, Peter Teufl and Gaby
   Whitehead for the feedback.  Also, everyone that have been working
   with Base64 over a long period of years and have proven the
   implementations are stable.

8.  Normative References

   [ISO18004]
              ISO/IEC JTC 1/SC 31, "ISO/IEC 18004:2015 Information
              technology - Automatic identification and data capture
              techniques - QR Code bar code symbology specification",
              ISO/IEC
              18004:2015 https://www.iso.org/standard/62021.html,
              February 2015.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

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   [RFC4648]  Josefsson, S., "The Base16, Base32, and Base64 Data
              Encodings", RFC 4648, DOI 10.17487/RFC4648, October 2006,
              <https://www.rfc-editor.org/info/rfc4648>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

Authors' Addresses

   Patrik Faltstrom
   Netnod

   Email: paf@netnod.se

   Fredrik Ljunggren
   Kirei

   Email: fredrik@kirei.se

   Dirk-Willem van Gulik
   Webweaving

   Email: dirkx@webweaving.org

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