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draft-ietf-cbor-packed-12

Document Type Active Internet-Draft (cbor WG)
Authors Carsten Bormann , Mikolai Gütschow
Last updated 2024-03-02
Replaces draft-bormann-cbor-packed
RFC stream Internet Engineering Task Force (IETF)
Intended RFC status Proposed Standard
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Stream WG state Waiting for WG Chair Go-Ahead
Revised I-D Needed - Issue raised by WGLC
Document shepherd Barry Leiba
Shepherd write-up Show Last changed 2022-05-19
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draft-ietf-cbor-packed-12
Network Working Group                                         C. Bormann
Internet-Draft                                    Universität Bremen TZI
Intended status: Standards Track                             M. Gütschow
Expires: 3 September 2024                                     TU Dresden
                                                            2 March 2024

                              Packed CBOR
                       draft-ietf-cbor-packed-12

Abstract

   The Concise Binary Object Representation (CBOR, RFC 8949 == STD 94)
   is a data format whose design goals include the possibility of
   extremely small code size, fairly small message size, and
   extensibility without the need for version negotiation.

   CBOR does not provide any forms of data compression.  CBOR data
   items, in particular when generated from legacy data models, often
   allow considerable gains in compactness when applying data
   compression.  While traditional data compression techniques such as
   DEFLATE (RFC 1951) can work well for CBOR encoded data items, their
   disadvantage is that the receiver needs to decompress the compressed
   form to make use of the data.

   This specification describes Packed CBOR, a simple transformation of
   a CBOR data item into another CBOR data item that is almost as easy
   to consume as the original CBOR data item.  A separate decompression
   step is therefore often not required at the receiver.

   // The present version (-12) updates the IANA "Values for Tag
   // Numbers" table, sorting it and cleaning up the "Data Item" column.

About This Document

   This note is to be removed before publishing as an RFC.

   Status information for this document may be found at
   https://datatracker.ietf.org/doc/draft-ietf-cbor-packed/.

   Discussion of this document takes place on the CBOR Working Group
   mailing list (mailto:cbor@ietf.org), which is archived at
   https://mailarchive.ietf.org/arch/browse/cbor/.  Subscribe at
   https://www.ietf.org/mailman/listinfo/cbor/.

   Source for this draft and an issue tracker can be found at
   https://github.com/cbor-wg/cbor-packed.

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Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on 3 September 2024.

Copyright Notice

   Copyright (c) 2024 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.
   Please review these documents carefully, as they describe your rights
   and restrictions with respect to this document.  Code Components
   extracted from this document must include Revised BSD License text as
   described in Section 4.e of the Trust Legal Provisions and are
   provided without warranty as described in the Revised BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Terminology and Conventions . . . . . . . . . . . . . . .   4
   2.  Packed CBOR . . . . . . . . . . . . . . . . . . . . . . . . .   5
     2.1.  Packing Tables  . . . . . . . . . . . . . . . . . . . . .   5
     2.2.  Referencing Shared Items  . . . . . . . . . . . . . . . .   6
     2.3.  Referencing Argument Items  . . . . . . . . . . . . . . .   7
     2.4.  Concatenation . . . . . . . . . . . . . . . . . . . . . .  10
     2.5.  Discussion  . . . . . . . . . . . . . . . . . . . . . . .  11
   3.  Table Setup . . . . . . . . . . . . . . . . . . . . . . . . .  12
     3.1.  Basic Packed CBOR . . . . . . . . . . . . . . . . . . . .  13
   4.  Function Tags . . . . . . . . . . . . . . . . . . . . . . . .  14
     4.1.  Join Function Tags  . . . . . . . . . . . . . . . . . . .  14
     4.2.  Record Function Tag . . . . . . . . . . . . . . . . . . .  15
   5.  Tag Validity: Tag Equivalence Principle . . . . . . . . . . .  16
     5.1.  Tag Equivalence . . . . . . . . . . . . . . . . . . . . .  17

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     5.2.  Tag Equivalence of Packed CBOR Tags . . . . . . . . . . .  18
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  18
     6.1.  CBOR Tags Registry  . . . . . . . . . . . . . . . . . . .  18
     6.2.  CBOR Simple Values Registry . . . . . . . . . . . . . . .  20
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  21
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  21
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .  21
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  22
   Appendix A.  Examples . . . . . . . . . . . . . . . . . . . . . .  22
   Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .  28
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  28

1.  Introduction

   The Concise Binary Object Representation (CBOR, [STD94]) is a data
   format whose design goals include the possibility of extremely small
   code size, fairly small message size, and extensibility without the
   need for version negotiation.

   CBOR does not provide any forms of data compression.  CBOR data
   items, in particular when generated from legacy data models, often
   allow considerable gains in compactness when applying data
   compression.  While traditional data compression techniques such as
   DEFLATE [RFC1951] can work well for CBOR encoded data items, their
   disadvantage is that the receiver needs to decompress the compressed
   form to make use of the data.

   This specification describes Packed CBOR, a simple transformation of
   a CBOR data item into another CBOR data item that is almost as easy
   to consume as the original CBOR data item.  A separate decompression
   step is therefore often not required at the receiver.

   This document defines the Packed CBOR format by specifying the
   transformation from a Packed CBOR data item to the original CBOR data
   item; it does not define an algorithm for a packer.  Different
   packers can differ in the amount of effort they invest in arriving at
   a minimal packed form; often, they simply employ the sharing that is
   natural for a specific application.

   Packed CBOR can make use of two kinds of optimization:

   *  item sharing: substructures (data items) that occur repeatedly in
      the original CBOR data item can be collapsed to a simple reference
      to a common representation of that data item.  The processing
      required during consumption is limited to following that
      reference.

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   *  argument sharing: application of a function with two arguments,
      one of which is shared.  Data items (strings, containers) that
      share a prefix or suffix, or more generally data items that can be
      constructed from a function taking a shared argument and a rump
      data item, can be replaced by a reference to the shared argument
      plus a rump data item.  For strings and the default
      "concatenation" function, the processing required during
      consumption is similar to following the argument reference plus
      that for an indefinite-length string.

   A specific application protocol that employs Packed CBOR might allow
   both kinds of optimization or limit the representation to item
   sharing only.

   Packed CBOR is defined in two parts: Referencing packing tables
   (Section 2) and setting up packing tables (Section 3).

1.1.  Terminology and Conventions

   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.

   Original data item:  A CBOR data item that is intended to be
      expressed by a packed data item; the result of all
      reconstructions.

   Packed data item:  A CBOR data item that involves packed references
      (_packed CBOR_).

   Packed reference:  A shared item reference or an argument reference.

   Shared item reference:  A reference to a shared item as defined in
      Section 2.2.

   Argument reference:  A reference that combines a shared argument with
      a rump item as defined in Section 2.3.

   Rump:  The data item contained in an argument reference that is
      combined with the argument to yield the reconstruction.

   Straight reference:  An argument reference that uses the argument as
      the left-hand side and the rump as the right-hand side.

   Inverted reference:  An argument reference that uses the rump as the
      left-hand side and the argument as the right-hand side.

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   Function tag:  A tag used in an argument reference for the argument
      (straight references) or the rump (inverted references), causing
      the application of a function indicated by the function tag in
      order to reconstruct the data item.

   Packing tables:  The pair of a shared item table and an argument
      table.

   Active set (of packing tables):  The packing tables in effect at the
      data item under consideration.

   Reconstruction:  The result of applying a packed reference in the
      context of given packing tables; we speak of the _reconstruction
      of a packed reference_ as that result.

   The definitions of [STD94] apply.  Specifically: The term "byte" is
   used in its now customary sense as a synonym for "octet"; "byte
   strings" are CBOR data items carrying a sequence of zero or more
   (binary) bytes, while "text strings" are CBOR data items carrying a
   sequence of zero or more Unicode code points (more precisely: Unicode
   scalar values), encoded in UTF-8 [STD63].

   Where arithmetic is explained, this document uses the notation
   familiar from the programming language C, except that ".." denotes a
   range that includes both ends given, in the HTML and PDF versions,
   subtraction and negation are rendered as a hyphen ("-", as are
   various dashes), and superscript notation denotes exponentiation.
   For example, 2 to the power of 64 is notated: 2^64.  In the plain-
   text version of this specification, superscript notation is not
   available and therefore is rendered by a surrogate notation.  That
   notation is not optimized for this RFC; it is unfortunately ambiguous
   with C's exclusive-or and requires circumspection from the reader of
   the plain-text version.

   Examples of CBOR data items are shown in CBOR Extended Diagnostic
   Notation (Section 8 of RFC 8949 [STD94] in conjunction with
   Appendix G of [RFC8610]).

2.  Packed CBOR

   This section describes the packing tables, their structure, and how
   they are referenced.

2.1.  Packing Tables

   At any point within a data item making use of Packed CBOR, there is
   an _active set_ of packing tables that applies.

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   There are two packing tables in an active set:

   *  Shared item table

   *  Argument table

   Without any table setup, these two tables are empty arrays.
   Table setup can cause these arrays to be non-empty, where the
   elements are (potentially themselves packed) data items.  Each of the
   tables is indexed by an unsigned integer (starting from 0).  Such an
   index may be derived from information in tags and their content as
   well as from CBOR simple values.

   Table setup mechanisms (see Section 3) may include all information
   needed for table setup within the packed CBOR data item, or they may
   refer to external information.  This information may be immutable, or
   it may be intended to potentially grow over time.  This raises the
   question of how a reference to a new item should be handled when the
   unpacker uses an older version of the external information.

   If, during unpacking, an index is used that references an item that
   is unpopulated in (e.g., outside the size of) the table in use, this
   MAY be treated as an error by the unpacker and abort the unpacking.
   Alternatively, the unpacker MAY provide the special value
   1112(undefined) (the simple value >undefined< as per Section 5.7 of
   RFC 8949 [STD94], enclosed in the tag 1112) to the application and
   leave the error handling to the application.  An unpacker SHOULD
   document which of these two alternatives has been chosen.  CBOR based
   protocols that include the use of packed CBOR MAY require that
   unpacking errors are tolerated in some positions.

2.2.  Referencing Shared Items

   Shared items are stored in the shared item table of the active set.

   The shared data items are referenced by using the reference data
   items in Table 1.  When reconstructing the original data item, such a
   reference is replaced by the referenced data item, which is then
   recursively unpacked.

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               +===========================+==============+
               | reference                 | table index  |
               +===========================+==============+
               | Simple value 0..15        | 0..15        |
               +---------------------------+--------------+
               | Tag 6(unsigned integer N) | 16 + 2*N     |
               +---------------------------+--------------+
               | Tag 6(negative integer N) | 16 - 2*N - 1 |
               +---------------------------+--------------+

                    Table 1: Referencing Shared Values

   As examples, the first 22 elements of the shared item table are
   referenced by simple(0), simple(1), ... simple(15), 6(0), 6(-1),
   6(1), 6(-2), 6(2), 6(-3).  (The alternation between unsigned and
   negative integers for even/odd table index values — "zigzag encoding"
   — makes systematic use of shorter integer encodings first.)

   Taking into account the encoding of these referring data items, there
   are 16 one-byte references, 48 two-byte references, 512 three-byte
   references, 131072 four-byte references, etc.  As CBOR integers can
   grow to very large (or very negative) values, there is no practical
   limit to how many shared items might be used in a Packed CBOR item.

   Note that the semantics of Tag 6 depend on its tag content: An
   integer turns the tag into a shared item reference, whereas a string
   or container (map or array) turns it into a straight (prefix)
   reference (see Table 2).  Note also that the tag content of Tag 6 may
   itself be packed, so it may need to be unpacked to make this
   determination.

2.3.  Referencing Argument Items

   The argument table serves as a common table that can be used for
   argument references, i.e., for concatenation as well as references
   involving a function tag.

   When referencing an argument, a distinction is made between straight
   and inverted references; if no function tag is involved, a straight
   reference combines a prefix out of the argument table with the rump
   data item, and an inverted reference combines a rump data item with a
   suffix out of the argument table.

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          +==================================+=================+
          | straight reference               |     table index |
          +==================================+=================+
          | Tag 6(rump)                      |               0 |
          +----------------------------------+-----------------+
          | Tag 224..255(rump)               |           0..31 |
          +----------------------------------+-----------------+
          | Tag 28704..32767(rump)           |        32..4095 |
          +----------------------------------+-----------------+
          | Tag 1879052288..2147483647(rump) | 4096..268435455 |
          +----------------------------------+-----------------+

          Table 2: Straight Referencing (e.g., Prefix) Arguments

           +==================================+================+
           | inverted reference               |    table index |
           +==================================+================+
           | Tag 216..223(rump)               |           0..7 |
           +----------------------------------+----------------+
           | Tag 27647..28671(rump)           |        8..1023 |
           +----------------------------------+----------------+
           | Tag 1811940352..1879048191(rump) | 1024..67108863 |
           +----------------------------------+----------------+

                Table 3: Inverted Referencing (e.g., Suffix)
                                 Arguments

   Argument data items are referenced by using the reference data items
   in Table 2 and Table 3.

   The tag number of the reference is used to derive a table index (an
   unsigned integer) leading to the "argument"; the tag content of the
   reference is the "rump item".

   When reconstructing the original data item, such a reference is
   replaced by a data item constructed from the argument data item found
   in the table (argument, which might need to be recursively unpacked
   first) and the rump data item (rump, again possibly needing to be
   recursively unpacked).

   Separate from the tag used as a reference, a tag ("function tag") may
   be involved to supply a function to be used in resolving the
   reference.  It is crucial not to confuse reference tag and, if
   present, function tag.

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   A straight reference uses the argument as the provisional left-hand
   side and the rump data item as the right-hand side.  An inverted
   reference uses the rump data item as the provisional left-hand side
   and the argument as the right-hand side.

   In both cases, the provisional left-hand side is examined.  If it is
   a tag ("function tag"), it is "unwrapped": The function tag's tag
   number is used to indicate the function to be applied, and the tag
   content is kept as the unwrapped left-hand side.  If the provisional
   left-hand side is not a tag, it is kept as the unwrapped left-hand
   side, and the function to be applied is concatenation, as defined
   below.  The right-hand side is taken as is as the unwrapped right-
   hand side.

   If a function tag was given, the reference is replaced by the result
   of applying the indicated unpacking function with the left-hand side
   as its first argument and the right-hand side as its second.  The
   unpacking function is defined by the definition of the tag number
   supplied.  If that definition does not define an unpacking function,
   the result of the unpacking is not valid.

   If no function tag was given, the reference is replaced by the left-
   hand side "concatenated" with the right-hand side, where
   concatenation is defined as in Section 2.4.

   As a contrived (but short) example, if the argument table is
   ["foobar", h'666f6f62', "fo"], each of the following straight
   (prefix) references will unpack to "foobart": 6("t"), 225("art"),
   226("obart") (the byte string h'666f6f62' == 'foob' is concatenated
   into a text string, and the last example is not an optimization).

   Note that table index 0 of the argument table can be referenced both
   with tag 6 and tag 224, however tag 6 with an integer content is used
   for shared item references (see Table 1), so to combine index 0 with
   an integer rump, tag 224 needs to be used.  The preferred encoding
   uses tag 6 if that is not necessary.

   Taking into account the encoding and ignoring the less optimal tag
   224, there is one single-byte straight (prefix) reference, 31
   (2^5-2^0) two-byte references, 4064 (2^12-2^5) three-byte references,
   and 26843160 (2^28-2^12) five-byte references for straight
   references. 268435455 (2^28) is an artificial limit, but should be
   high enough that there, again, is no practical limit to how many
   prefix items might be used in a Packed CBOR item.  The numbers for
   inverted (suffix) references are one quarter of those, except that
   there is no single-byte reference and 8 two-byte references.

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      |  Rationale: Experience suggests that straight (prefix) packing
      |  might be more likely than inverted (suffix) packing.  Also for
      |  this reason, there is no intent to spend a 1+0 tag value for
      |  inverted packing.

2.4.  Concatenation

   The concatenation function is defined as follows:

   *  If both left-hand side and right-hand side are arrays, the result
      of the concatenation is an array with all elements of the left-
      hand-side array followed by the elements of the right-hand side
      array.

   *  If both left-hand side and right-hand side are maps, the result of
      the concatenation is a map that is initialized with a copy of the
      left-hand-side map, and then filled in with the members of the
      right-hand side map, replacing any existing members that have the
      same key.  In order to be able to remove a map entry from the
      left-hand-side map, as a special case, any members to be replaced
      with a value of undefined (0xf7) from the right-hand-side map are
      instead removed, and right-hand-side members with the value
      undefined are never filled in into the concatenated map.

      |  NOTES:
      |  
      |     *  One application of the rule for straight references is to
      |        supply default values out of a dictionary, which can then
      |        be overridden by the entries in the map supplied as the
      |        rump data item.
      |  
      |     *  Special casing the member value undefined makes it
      |        impossible to use this construct for updating maps by
      |        insertion of or replacement with actual undefined member
      |        values; undefined as a member value on the left-hand-side
      |        map stays untouched though.  This exception is similar to
      |        the one JSON Merge Patch [RFC7396] makes for null values,
      |        which are however much more commonly used and therefore
      |        more problematic.

   *  If both left-hand side and right-hand side are one of the string
      types (not necessarily the same), the bytes of the left-hand side
      are concatenated with the bytes of the right-hand side.  Byte
      strings concatenated with text strings need to contain valid UTF-8
      data.  The result of the concatenation gets the type of the
      unwrapped rump data item; this way a single argument table entry
      can be used to build both byte and text strings, depending on what
      type of rump is being used.

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   *  If one side is one of the string types, and the other side is an
      array, the result of the concatenation is equivalent to the
      application of the "join" function (Section 4.1) to the string as
      the left-hand side and the array as the right-hand side.  The
      original right-hand side of the concatenation determines the
      string type of the result.

   *  Other type combinations of left-hand side and right-hand side are
      not valid.

2.5.  Discussion

   This specification uses up a large number of Simple Values and Tags,
   in particular one of the rare one-byte tags and two thirds of the
   one-byte simple values.  Since the objective is compression, this is
   warranted only based on a consensus that this specific format could
   be useful for a wide area of applications, while maintaining
   reasonable simplicity in particular at the side of the consumer.

   A maliciously crafted Packed CBOR data item might contain a reference
   loop.  A consumer/decompressor MUST protect against that.

      |  Different strategies for decoding/consuming Packed CBOR are
      |  available.
      |  For example:
      |  
      |     *  the decoder can decode and unpack the packed item,
      |        presenting an unpacked data item to the application.  In
      |        this case, the onus of dealing with loops is on the
      |        decoder.  (This strategy generally has the highest memory
      |        consumption, but also the simplest interface to the
      |        application.)  Besides avoiding getting stuck in a
      |        reference loop, the decoder will need to control its
      |        resource allocation, as data items can "blow up" during
      |        unpacking.
      |  
      |     *  the decoder can be oblivious of Packed CBOR.  In this
      |        case, the onus of dealing with loops is on the
      |        application, as is the entire onus of dealing with Packed
      |        CBOR.
      |  
      |     *  hybrid models are possible, for instance: The decoder
      |        builds a data item tree directly from the Packed CBOR as
      |        if it were oblivious, but also provides accessors that
      |        hide (resolve) the packing.  In this specific case, the
      |        onus of dealing with loops is on the accessors.
      |  

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      |  In general, loop detection can be handled in a similar way in
      |  which loops of symbolic links are handled in a file system: A
      |  system-wide limit (often set to a value permitting some 20 to
      |  40 indirections for symbolic links) is applied to any reference
      |  chase.

      |  NOTE: The present specification does nothing to help with the
      |  packing of CBOR sequences [RFC8742]; maybe such a specification
      |  should be added.

3.  Table Setup

   The packing references described in Section 2 assume that packing
   tables have been set up.

   By default, both tables are empty (zero-length arrays).

   Table setup can happen in one of two ways:

   *  By the application environment, e.g., a media type.  These can
      define tables that amount to a static dictionary that can be used
      in a CBOR data item for this application environment.  Note that,
      without this information, a data item that uses such a static
      dictionary can be decoded at the CBOR level, but not fully
      unpacked.  The table setup mechanisms provided by this document
      are defined in such a way that an unpacker can at least recognize
      if this is the case.

   *  By one or more _table-building_ tags enclosing the packed content.
      Each tag is usually defined to build an augmented table by adding
      to the packing tables that already apply to the tag, and to apply
      the resulting augmented table when unpacking the tag content.
      Usually, the semantics of the tag will be to prepend items to one
      or more of the tables.  (The specific behavior of any such tag, in
      the presence of a table applying to it, needs to be carefully
      specified.)

      Note that it may be useful to leave a particular efficiency tier
      alone and only prepend to a higher tier; e.g., a tag could insert
      shared items at table index 16 and shift anything that was already
      there further along in the array while leaving index 0 to 15
      alone.  Explicit additions by tag can combine with application-
      environment supplied tables that apply to the entire CBOR data
      item.

      Packed item references in the newly constructed (low-numbered)
      parts of the table are usually interpreted in the number space of
      that table (which includes the, now higher-numbered, inherited

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      parts), while references in any existing, inherited (higher-
      numbered) part continue to use the (more limited) number space of
      the inherited table.

   Where external information is used in a table setup mechanism that is
   not immutable, care needs to be taken so that, over time, references
   to existing table entries stay valid (i.e., the information is only
   extended), and that a maximum size of this information is given.
   This allows an unpacker to recognize references to items that are not
   yet defined in the version of the external reference that it uses,
   providing backward and possibly limited (degraded) forward
   compatibility.

   For table setup, the present specification only defines two simple
   table-building tags, which operate by prepending to the (by default
   empty) tables.

      |  Additional tags can be defined for dictionary referencing
      |  (possible combining that with Basic Packed CBOR mechanisms).
      |  The desirable details are likely to vary considerably between
      |  applications.  A URI-based reference would be easy to define,
      |  but might be too inefficient when used in the likely
      |  combination with an ni: URI [RFC6920].

3.1.  Basic Packed CBOR

   Two tags are predefined by this specification for packing table
   setup.  They are defined in CDDL [RFC8610] as in Figure 1:

   Basic-Packed-CBOR = #6.113([[*shared-and-argument-item], rump])
   Split-Basic-Packed-CBOR =
                       #6.1113([[*shared-item], [*argument-item], rump])
   rump = any
   shared-and-argument-item = any
   argument-item = any
   shared-item = any

                       Figure 1: Packed CBOR in CDDL

   (This assumes the allocation of tag numbers 113 ('q') and 1113 for
   these tags.)

   The array given as the first element of the content of tag 113
   ("Basic-Packed-CBOR") is prepended to both the tables for shared
   items and arguments that apply to the entire tag (by default empty
   tables).  The arrays given as the first and second element of the
   content of the tag 1113 ("Split-Basic-Packed-CBOR") are prepended to
   the tables for shared items and arguments, respectively, that apply

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   to the entire tag (by default empty tables).  As discussed in the
   introduction to this section, references in the supplied new arrays
   use the new number space (where inherited items are shifted by the
   new items given), while the inherited items themselves use the
   inherited number space (so their semantics do not change by the mere
   action of inheritance).

   The original CBOR data item can be reconstructed by recursively
   replacing shared and argument references encountered in the rump by
   their reconstructions.

4.  Function Tags

   Function tags that occur in an argument or a rump supply the
   semantics for reconstructing a data item from their tag content and
   the non-dominating rump or argument, respectively.  The present
   specification defines three function tags.

4.1.  Join Function Tags

   Tag 106 ('j') defines the "join" unpacking function, based on the
   concatenation function (Section 2.4).

   The join function expects an item that can be concatenated as its
   left-hand side, and an array of such items as its right-hand side.
   Joining works by sequentially applying the concatenation function to
   the elements of the right-hand-side array, interspersing the left-
   hand side as the "joiner".

   An example in functional notation: join(", ", ["a", "b", "c"])
   returns "a, b, c".

   For a right-hand side of one or more elements, the first element
   determines the type of the result when text strings and byte strings
   are mixed in the argument.  For a right-hand side of one element, the
   joiner is not used, and that element returned.  For a right-hand side
   of zero elements, a neutral element is generated based on the type of
   the joiner (empty text/byte string for a text/byte string, empty
   array for an array, empty map for a map).

   For an example, we assume this unpacked data item:

   ["https://packed.example/foo.html",
    "coap:://packed.example/bar.cbor",
    "mailto:support@packed.example"]

   A packed form of this using straight references could be:

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   113([[106("packed.example")],
     [6(["https://", "/foo.html"]),
      6(["coap://", "/bar.cbor"]),
      6(["mailto:support@", ""])]
   ])

   Tag 105 ('i') defines the "ijoin" unpacking function, which is
   exactly like that of tag 106, except that the left-hand side and
   right-hand side are interchanged ('i').

   A packed form of the first example using inverted references and the
   ijoin tag could be:

   113([["packed.example"],
     [216(105(["https://", "/foo.html"])),
      216(105(["coap://", "/bar.cbor"])),
      216("mailto:support@")]
   ])

   A packed form of an array with many URIs that reference SenML items
   from the same place could be:

   113([[105(["coaps://[2001::db8::1]/s/", ".senml"])],
     [6("temp-freezer"),
      6("temp-fridge"),
      6("temp-ambient")]
   ])

   Note that for these examples, the implicit join semantics for mixed
   string-array concatenation as defined in Section 2.4, Paragraph 5
   actually obviate the need for an explicit join/ijoin tag; the
   examples do serve to demonstrate the explicit usage of the tag.

4.2.  Record Function Tag

   Tag 114 ('r') defines the "record" function, which combines an array
   of keys with an array of values into a map.

   The record function expects an array as its left-hand side, whose
   items are treated as key items for the resulting map, and an array of
   equal or shorter length as its right-hand side, whose items are
   treated as value items for the resulting map.

   The map is constructed by grouping key and value items with equal
   position in the provided arrays into pairs that constitute the
   resulting map.

   The value item array MUST NOT be longer than the key item array.

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   The value item array MAY be shorter than the key item array, in which
   case the one or more unmatched value items towards the end are
   treated as _absent_. Additionally, value items that are the CBOR
   simple value undefined (simple(23), encoding 0xf7) are also treated
   as absent.  Key items whose matching value items are absent are not
   included in the resulting map.

   For an example, we assume this unpacked data item:

   [{"key0": false, "key1": "value 1", "key2": 2},
    {"key0": true, "key1": "value -1", "key2": -2},
    {"key1": "", "key2": 0}]

   A straightforward packed form of this using the record function tag
   could be:

   113([[114(["key0", "key1", "key2"])],
     [6([false, "value 1", 2]),
      6([true, "value -1", -2]),
      6([undefined, "", 0])]
   ])

   A slightly more concise packed form can be achieved by manipulating
   the key item order (recall that the order of key/value pairs in maps
   carries no semantics):

   113([[114(["key1", "key2", "key0"])],
     [6(["value 1", 2, false]),
      6(["value -1", -2, true]),
      6(["", 0])]
   ])

5.  Tag Validity: Tag Equivalence Principle

   In Section 5.3.2 of RFC 8949 [STD94], the validity of tags is defined
   in terms of type and value of their tag content.  The CBOR Tag
   registry ([IANA.cbor-tags] as defined in Section 9.2 of RFC 8949
   [STD94]) allows recording the "data item" for a registered tag, which
   is usually an abbreviated description of the top-level data type
   allowed for the tag content.

   In other words, in the registry, the validity of a tag of a given tag
   number is described in terms of the top-level structure of the data
   carried in the tag content.  The description of a tag might add
   further constraints for the data item.  But in any case, a tag
   definition can only specify validity based on the structure of its
   tag content.

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   In Packed CBOR, a reference tag might be "standing in" for the actual
   tag content of an outer tag, or for a structural component of that.
   In this case, the formal structure of the outer tag's content before
   unpacking usually no longer fulfills the validity conditions of the
   outer tag.

   The underlying problem is not unique to Packed CBOR.  For instance,
   [RFC8746] describes tags 64..87 that "stand in" for CBOR arrays (the
   native form of which has major type 4).  For the other tags defined
   in this specification, which require some array structure of the tag
   content, a footnote was added:

   |  [...] The second element of the outer array in the data item is a
   |  native CBOR array (major type 4) or Typed Array (one of tag
   |  64..87)

   The top-down approach to handle the "rendezvous" between the outer
   and inner tags does not support extensibility: any further Typed
   Array tags being defined do not inherit the exception granted to tag
   number 64..87; they would need to formally update all existing tag
   definitions that can accept typed arrays or be of limited use with
   these existing tags.

   Instead, the tag validity mechanism needs to be extended by a bottom-
   up component: A tag definition needs to be able to declare that the
   tag can "stand in" for, (is, in terms of tag validity, equivalent to)
   some structure.

   E.g., tag 64..87 could have declared their equivalence to the CBOR
   major type 4 arrays they stand in for.

      |  Note that not all domain extensions to tags can be addressed
      |  using the equivalence principle: E.g., on a data model level,
      |  numbers with arbitrary exponents ([ARB-EXP], tags 264 and 265)
      |  are strictly a superset of CBOR's predefined fractional types,
      |  tags 4 and 5.  They could not simply declare that they are
      |  equivalent to tags 4 and 5 as a tag requiring a fractional
      |  value may have no way to handle the extended range of tag 264
      |  and 265.

5.1.  Tag Equivalence

   A tag definition MAY declare Tag Equivalence to some existing
   structure for the tag, under some conditions defined by the new tag
   definition.  This, in effect, extends all existing tag definitions
   that accept the named structure to accept the newly defined tag under
   the conditions given for the Tag Equivalence.

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   A number of limitations apply to Tag Equivalence, which therefore
   should be applied deliberately and sparingly:

   *  Tag Equivalence is a new concept, which may not be implemented by
      an existing generic decoder.  A generic decoder not implementing
      tag equivalence might raise tag validity errors where Tag
      Equivalence says there should be none.

   *  A CBOR protocol MAY specify the use of Tag Equivalence,
      effectively limiting its full use to those generic encoders that
      implement it.  Existing CBOR protocols that do not address Tag
      Equivalence implicitly have a new variant that allows Tag
      Equivalence (e.g., to support Packed CBOR with an existing
      protocol).  A CBOR protocol that does address Tag Equivalence MAY
      be explicit about what kinds of Tag Equivalence it supports (e.g.,
      only the reference tags employed by Packed CBOR and certain table
      setup tags).

   *  There is currently no way to express Tag Equivalence in CDDL.  For
      Packed CBOR, CDDL would typically be used to describe the unpacked
      CBOR represented by it; further restricting the Packed CBOR is
      likely to lead to interoperability problems.  (Note that, by
      definition, there is no need to describe Tag Equivalence on the
      receptacle side; only for the tag that declares Tag Equivalence.)

   *  The registry "CBOR Tags" [IANA.cbor-tags] currently does not have
      a way to record any equivalence claimed for a tag.  A convention
      would be to alert to Tag Equivalence in the "Semantics (short
      form)" field of the registry.
      // Needs to be done for the tag registrations here.

5.2.  Tag Equivalence of Packed CBOR Tags

   The reference tags in this specification declare their equivalence to
   the unpacked shared items or function results they represent.

   The table setup tags 113 and 1113 declare its equivalence to the
   unpacked CBOR data item represented by it.

6.  IANA Considerations

6.1.  CBOR Tags Registry

   In the registry "CBOR Tags" [IANA.cbor-tags], IANA is requested to
   allocate the tags defined in Table 4.

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   +========================+=================+===========+===========+
   |                    Tag | Data Item       | Semantics | Reference |
   +========================+=================+===========+===========+
   |                      6 | integer (for    | Packed    | draft-    |
   |                        | shared); any    | CBOR:     | ietf-     |
   |                        | except integer  | shared/   | cbor-     |
   |                        | (for straight)  | straight  | packed    |
   +------------------------+-----------------+-----------+-----------+
   |                    105 | concatenation   | Packed    | draft-    |
   |                        | item (text      | CBOR:     | ietf-     |
   |                        | string, byte    | ijoin     | cbor-     |
   |                        | string, array,  | function  | packed    |
   |                        | or map)         |           |           |
   +------------------------+-----------------+-----------+-----------+
   |                    106 | array of        | Packed    | draft-    |
   |                        | concatenation   | CBOR:     | ietf-     |
   |                        | item (text      | join      | cbor-     |
   |                        | string, byte    | function  | packed    |
   |                        | string, array,  |           |           |
   |                        | or map)         |           |           |
   +------------------------+-----------------+-----------+-----------+
   |                    113 | array (shared-  | Packed    | draft-    |
   |                        | and-argument-   | CBOR:     | ietf-     |
   |                        | items, rump)    | table     | cbor-     |
   |                        |                 | setup     | packed    |
   +------------------------+-----------------+-----------+-----------+
   |                    114 | array           | Packed    | draft-    |
   |                        |                 | CBOR:     | ietf-     |
   |                        |                 | record    | cbor-     |
   |                        |                 | function  | packed    |
   +------------------------+-----------------+-----------+-----------+
   |               216..223 | function tag or | Packed    | draft-    |
   |                        | concatenation   | CBOR:     | ietf-     |
   |                        | item (text      | inverted  | cbor-     |
   |                        | string, byte    |           | packed    |
   |                        | string, array,  |           |           |
   |                        | or map)         |           |           |
   +------------------------+-----------------+-----------+-----------+
   |               224..255 | any             | Packed    | draft-    |
   |                        |                 | CBOR:     | ietf-     |
   |                        |                 | straight  | cbor-     |
   |                        |                 |           | packed    |
   +------------------------+-----------------+-----------+-----------+
   |                   1112 | undefined       | Packed    | draft-    |
   |                        | (0xf7)          | CBOR:     | ietf-     |
   |                        |                 | reference | cbor-     |
   |                        |                 | error     | packed    |
   +------------------------+-----------------+-----------+-----------+

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   |                   1113 | array (shared-  | Packed    | draft-    |
   |                        | items,          | CBOR:     | ietf-     |
   |                        | argument-items, | table     | cbor-     |
   |                        | rump)           | setup     | packed    |
   +------------------------+-----------------+-----------+-----------+
   |           27647..28671 | function tag or | Packed    | draft-    |
   |                        | concatenation   | CBOR:     | ietf-     |
   |                        | item (text      | inverted  | cbor-     |
   |                        | string, byte    |           | packed    |
   |                        | string, array,  |           |           |
   |                        | or map)         |           |           |
   +------------------------+-----------------+-----------+-----------+
   |           28704..32767 | any             | Packed    | draft-    |
   |                        |                 | CBOR:     | ietf-     |
   |                        |                 | straight  | cbor-     |
   |                        |                 |           | packed    |
   +------------------------+-----------------+-----------+-----------+
   | 1811940352..1879048191 | function tag or | Packed    | draft-    |
   |                        | concatenation   | CBOR:     | ietf-     |
   |                        | item (text      | inverted  | cbor-     |
   |                        | string, byte    |           | packed    |
   |                        | string, array,  |           |           |
   |                        | or map)         |           |           |
   +------------------------+-----------------+-----------+-----------+
   | 1879052288..2147483647 | any             | Packed    | draft-    |
   |                        |                 | CBOR:     | ietf-     |
   |                        |                 | straight  | cbor-     |
   |                        |                 |           | packed    |
   +------------------------+-----------------+-----------+-----------+

                     Table 4: Values for Tag Numbers

6.2.  CBOR Simple Values Registry

   In the registry "CBOR Simple Values" [IANA.cbor-simple-values], IANA
   is requested to allocate the simple values defined in Table 5.

         +=======+=====================+========================+
         | Value | Semantics           | Reference              |
         +=======+=====================+========================+
         | 0..15 | Packed CBOR: shared | draft-ietf-cbor-packed |
         +-------+---------------------+------------------------+

                          Table 5: Simple Values

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7.  Security Considerations

   The security considerations of [STD94] apply.

   Loops in the Packed CBOR can be used as a denial of service attack,
   see Section 2.5.

   As the unpacking is deterministic, packed forms can be used as
   signing inputs.  (Note that if external dictionaries are added to
   cbor-packed, this requires additional consideration.)

8.  References

8.1.  Normative References

   [IANA.cbor-simple-values]
              IANA, "Concise Binary Object Representation (CBOR) Simple
              Values",
              <https://www.iana.org/assignments/cbor-simple-values>.

   [IANA.cbor-tags]
              IANA, "Concise Binary Object Representation (CBOR) Tags",
              <https://www.iana.org/assignments/cbor-tags>.

   [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/rfc/rfc2119>.

   [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/rfc/rfc8174>.

   [RFC8610]  Birkholz, H., Vigano, C., and C. Bormann, "Concise Data
              Definition Language (CDDL): A Notational Convention to
              Express Concise Binary Object Representation (CBOR) and
              JSON Data Structures", RFC 8610, DOI 10.17487/RFC8610,
              June 2019, <https://www.rfc-editor.org/rfc/rfc8610>.

   [STD94]    Internet Standard 94,
              <https://www.rfc-editor.org/info/std94>.
              At the time of writing, this STD comprises the following:

              Bormann, C. and P. Hoffman, "Concise Binary Object
              Representation (CBOR)", STD 94, RFC 8949,
              DOI 10.17487/RFC8949, December 2020,
              <https://www.rfc-editor.org/info/rfc8949>.

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8.2.  Informative References

   [ARB-EXP]  Occil, P., "Arbitrary-Exponent Numbers", Specification for
              Registration of CBOR Tags 264 and 265,
              <http://peteroupc.github.io/CBOR/bigfrac.html>.

   [RFC1951]  Deutsch, P., "DEFLATE Compressed Data Format Specification
              version 1.3", RFC 1951, DOI 10.17487/RFC1951, May 1996,
              <https://www.rfc-editor.org/rfc/rfc1951>.

   [RFC6920]  Farrell, S., Kutscher, D., Dannewitz, C., Ohlman, B.,
              Keranen, A., and P. Hallam-Baker, "Naming Things with
              Hashes", RFC 6920, DOI 10.17487/RFC6920, April 2013,
              <https://www.rfc-editor.org/rfc/rfc6920>.

   [RFC7049]  Bormann, C. and P. Hoffman, "Concise Binary Object
              Representation (CBOR)", RFC 7049, DOI 10.17487/RFC7049,
              October 2013, <https://www.rfc-editor.org/rfc/rfc7049>.

   [RFC7396]  Hoffman, P. and J. Snell, "JSON Merge Patch", RFC 7396,
              DOI 10.17487/RFC7396, October 2014,
              <https://www.rfc-editor.org/rfc/rfc7396>.

   [RFC8742]  Bormann, C., "Concise Binary Object Representation (CBOR)
              Sequences", RFC 8742, DOI 10.17487/RFC8742, February 2020,
              <https://www.rfc-editor.org/rfc/rfc8742>.

   [RFC8746]  Bormann, C., Ed., "Concise Binary Object Representation
              (CBOR) Tags for Typed Arrays", RFC 8746,
              DOI 10.17487/RFC8746, February 2020,
              <https://www.rfc-editor.org/rfc/rfc8746>.

   [STD63]    Internet Standard 63,
              <https://www.rfc-editor.org/info/std63>.
              At the time of writing, this STD comprises the following:

              Yergeau, F., "UTF-8, a transformation format of ISO
              10646", STD 63, RFC 3629, DOI 10.17487/RFC3629, November
              2003, <https://www.rfc-editor.org/info/rfc3629>.

Appendix A.  Examples

   The (JSON-compatible) CBOR data structure depicted in Figure 2, 400
   bytes of binary CBOR, could be packed into the CBOR data item
   depicted in Figure 3, 308 bytes, only employing item sharing.  With
   support for argument sharing and the record function tag 114, the
   data item can be packed into 298 bytes as depicted in Figure 4.  Note
   that this particular example does not lend itself to prefix

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   compression, so it uses the simple common-table setup form (tag 113).

   { "store": {
       "book": [
         { "category": "reference",
           "author": "Nigel Rees",
           "title": "Sayings of the Century",
           "price": 8.95
         },
         { "category": "fiction",
           "author": "Evelyn Waugh",
           "title": "Sword of Honour",
           "price": 12.99
         },
         { "category": "fiction",
           "author": "Herman Melville",
           "title": "Moby Dick",
           "isbn": "0-553-21311-3",
           "price": 8.95
         },
         { "category": "fiction",
           "author": "J. R. R. Tolkien",
           "title": "The Lord of the Rings",
           "isbn": "0-395-19395-8",
           "price": 22.99
         }
       ],
       "bicycle": {
         "color": "red",
         "price": 19.95
       }
     }
   }

            Figure 2: Example original CBOR data item, 400 bytes

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   113([["price", "category", "author", "title", "fiction", 8.95,
                                                                "isbn"],
       /  0          1         2         3         4         5    6   /
        {"store": {
          "book": [
            {simple(1): "reference", simple(2): "Nigel Rees",
             simple(3): "Sayings of the Century", simple(0): simple(5)},
            {simple(1): simple(4), simple(2): "Evelyn Waugh",
             simple(3): "Sword of Honour", simple(0): 12.99},
            {simple(1): simple(4), simple(2): "Herman Melville",
             simple(3): "Moby Dick", simple(6): "0-553-21311-3",
             simple(0): simple(5)},
            {simple(1): simple(4), simple(2): "J. R. R. Tolkien",
             simple(3): "The Lord of the Rings",
             simple(6): "0-395-19395-8", simple(0): 22.99}],
          "bicycle": {"color": "red", simple(0): 19.95}}}])

      Figure 3: Example packed CBOR data item with item sharing only,
                                 308 bytes

   113([[114(["category", "author",
              "title", simple(1), "isbn"]),
       /  0                       /
         "price", "fiction", 8.95],
       /  1        2         3    /
        {"store": {
          "book": [
              6(["reference", "Nigel Rees",
                 "Sayings of the Century", simple(3)]),
              6([simple(2), "Evelyn Waugh",
                 "Sword of Honour", 12.99]),
              6([simple(2), "Herman Melville",
                 "Moby Dick", simple(3), "0-553-21311-3"]),
              6([simple(2), "J. R. R. Tolkien",
                  "The Lord of the Rings", 22.99, "0-395-19395-8"])],
          "bicycle": {"color": "red", simple(1): 19.95}}}])

       Figure 4: Example packed CBOR data item using item sharing and
                     the record function tag, 298 bytes

   The (JSON-compatible) CBOR data structure below has been packed with
   shared item and (partial) prefix compression only and employs the
   split-table setup form (tag 1113).

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   {
     "name": "MyLED",
     "interactions": [
       {
         "links": [
           {
             "href":
              "http://192.168.1.103:8445/wot/thing/MyLED/rgbValueRed",
             "mediaType": "application/json"
           }
         ],
         "outputData": {
           "valueType": {
             "type": "number"
           }
         },
         "name": "rgbValueRed",
         "writable": true,
         "@type": [
           "Property"
         ]
       },
       {
         "links": [
           {
             "href":
              "http://192.168.1.103:8445/wot/thing/MyLED/rgbValueGreen",
             "mediaType": "application/json"
           }
         ],
         "outputData": {
           "valueType": {
             "type": "number"
           }
         },
         "name": "rgbValueGreen",
         "writable": true,
         "@type": [
           "Property"
         ]
       },
       {
         "links": [
           {
             "href":
              "http://192.168.1.103:8445/wot/thing/MyLED/rgbValueBlue",
             "mediaType": "application/json"
           }

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         ],
         "outputData": {
           "valueType": {
             "type": "number"
           }
         },
         "name": "rgbValueBlue",
         "writable": true,
         "@type": [
           "Property"
         ]
       },
       {
         "links": [
           {
             "href":
              "http://192.168.1.103:8445/wot/thing/MyLED/rgbValueWhite",
             "mediaType": "application/json"
           }
         ],
         "outputData": {
           "valueType": {
             "type": "number"
           }
         },
         "name": "rgbValueWhite",
         "writable": true,
         "@type": [
           "Property"
         ]
       },
       {
         "links": [
           {
             "href":
              "http://192.168.1.103:8445/wot/thing/MyLED/ledOnOff",
             "mediaType": "application/json"
           }
         ],
         "outputData": {
           "valueType": {
             "type": "boolean"
           }
         },
         "name": "ledOnOff",
         "writable": true,
         "@type": [
           "Property"

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         ]
       },
       {
         "links": [
           {
             "href":
   "http://192.168.1.103:8445/wot/thing/MyLED/colorTemperatureChanged",
             "mediaType": "application/json"
           }
         ],
         "outputData": {
           "valueType": {
             "type": "number"
           }
         },
         "name": "colorTemperatureChanged",
         "@type": [
           "Event"
         ]
       }
     ],
     "@type": "Lamp",
     "id": "0",
     "base": "http://192.168.1.103:8445/wot/thing",
     "@context":
      "http://192.168.1.102:8444/wot/w3c-wot-td-context.jsonld"
   }

           Figure 5: Example original CBOR data item, 1210 bytes

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   1113([/shared/["name", "@type", "links", "href", "mediaType",
               /  0       1       2        3         4 /
       "application/json", "outputData", {"valueType": {"type":
            /  5               6               7 /
       "number"}}, ["Property"], "writable", "valueType", "type"],
                  /   8            9           10           11 /
      /argument/ ["http://192.168.1.10", 6("3:8445/wot/thing"),
                 / 6                        225 /
      225("/MyLED/"), 226("rgbValue"), "rgbValue",
        / 226             227           228     /
      {simple(6): simple(7), simple(9): true, simple(1): simple(8)}],
        / 229 /
      /rump/ {simple(0): "MyLED",
              "interactions": [
      229({simple(2): [{simple(3): 227("Red"), simple(4): simple(5)}],
       simple(0): 228("Red")}),
      229({simple(2): [{simple(3): 227("Green"), simple(4): simple(5)}],
       simple(0): 228("Green")}),
      229({simple(2): [{simple(3): 227("Blue"), simple(4): simple(5)}],
       simple(0): 228("Blue")}),
      229({simple(2): [{simple(3): 227("White"), simple(4): simple(5)}],
       simple(0): "rgbValueWhite"}),
      {simple(2): [{simple(3): 226("ledOnOff"), simple(4): simple(5)}],
       simple(6): {simple(10): {simple(11): "boolean"}}, simple(0):
       "ledOnOff", simple(9): true, simple(1): simple(8)},
      {simple(2): [{simple(3): 226("colorTemperatureChanged"),
       simple(4): simple(5)}], simple(6): simple(7), simple(0):
       "colorTemperatureChanged", simple(1): ["Event"]}],
        simple(1): "Lamp", "id": "0", "base": 225(""),
        "@context": 6("2:8444/wot/w3c-wot-td-context.jsonld")}])

             Figure 6: Example packed CBOR data item, 505 bytes

Acknowledgements

   CBOR packing was part of the original proposal that turned into CBOR,
   but did not make it into [RFC7049], the predecessor of RFC 8949
   [STD94].  Various attempts to come up with a specification over the
   years did not proceed.  In 2017, Sebastian Käbisch proposed
   investigating compact representations of W3C Thing Descriptions,
   which prompted the author to come up with what turned into the
   present design.

   This work was supported in part by the German Federal Ministry of
   Education and Research (BMBF) within the project Concrete Contracts.

Authors' Addresses

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   Carsten Bormann
   Universität Bremen TZI
   Postfach 330440
   D-28359 Bremen
   Germany
   Phone: +49-421-218-63921
   Email: cabo@tzi.org

   Mikolai Gütschow
   TUD Dresden University of Technology
   Helmholtzstr. 10
   D-01069 Dresden
   Germany
   Email: mikolai.guetschow@tu-dresden.de

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