The Base45 Data Encoding
draft-faltstrom-base45-06
Network Working Group P. Faltstrom
Internet-Draft Netnod
Intended status: Standards Track F. Ljunggren
Expires: December 16, 2021 Kirei
D. van Gulik
Webweaving
June 14, 2021
The Base45 Data Encoding
draft-faltstrom-base45-06
Abstract
This document describes the Base45 encoding scheme which is built
upon the Base64, Base32 and Base16 encoding schemes.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on December 16, 2021.
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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 use Base45 . . . . . . . . . . . . . . . . . . . 3
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 . . . . . . . . . . . . . . . . . . . . . . . 6
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 exists, e.g. Numeric, Alphanumeric and Byte mode. Even in Byte
mode a typical QR-code reader tries to interpret a byte sequence as
an 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 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", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
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
A 45-character subset of US-ASCII is used; the 45 characters usable
in a QR code in Alphanumeric mode. 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 an 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 bit. 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 are 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 is encoded on two characters as described above.
For decoding a Base45 encoded string the inverse operations are
performed.
4.1. When to use Base45
If binary data is to be stored in a QR-Code one possible way 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.
If the data is to be sent via some other transport, a transport
encoding suitable for that transport should be used instead of
Base45. It is not recommended to first encode data in Base45 and
then encode the resulting string in for example 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.
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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
value, it is [18533 27756 28449 33]. Note the 33 for the last byte.
When looking at the values modulo 45, we get [[38 6 9] [36 31 13] [9
2 14] [33 0]] where the last byte is represented by two. By looking
up these values in the Table 1 we get the encoded string "%69
VD92EX0".
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 modulo 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".
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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 at the
numbers in chunks of three, except last 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 for modulo 45 and lookup in the
table of characters (Table 1). A decoder also must 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, Base45 specifically avoids padding. Because of this,
special care has to be taken when odd number of octets are to be
encoded, which results not in N*3 characters, but (N-1)*3+2
characters in the encoded string and similarly, at decoding, when the
number of encoded characters 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
sent in order to exploit implementation errors leading to, e.g.,
buffer overflow attacks.
Implementations MUST reject the 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 the following case has to be considered: The
string "FGW" represents 65535 (FFFF in base 16), which is a valid
encoding. The string "GGW" would represent 65536 (10000 in base 16),
which is represented by more than 16 bit.
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Implementations MUST reject the encoded data if it contains a triplet
of characters which, when decoded, result in an unsigned integer
which is greater then 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 have to be URL safe, one have to use %-encoding.
7. Acknowledgements
The authors thank Alan Barrett, Alfred Fiedler, Tomas Harreveld,
Joakim Jardenberg, 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 implementions 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>.
[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>.
Authors' Addresses
Patrik Faltstrom
Netnod
Email: paf@netnod.se
Fredrik Ljunggren
Kirei
Email: fredrik@kirei.se
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Dirk-Willem van Gulik
Webweaving
Email: dirkx@webweaving.org
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