





Network Working Group                                            G. Klyne
Request for Comments: 2938                           Content Technologies
Updates: 2533                                                 L. Masinter
Category: Standards Track                                            AT&T
                                                           September 2000


                  Identifying Composite Media Features

Status of this Memo

   This document specifies an Internet standards track protocol for the
   Internet community, and requests discussion and suggestions for
   improvements.  Please refer to the current edition of the "Internet
   Official Protocol Standards" (STD 1) for the standardization state
   and status of this protocol.  Distribution of this memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (2000).  All Rights Reserved.

Abstract

   In RFC 2533, an expression format is presented for describing media
   feature capabilities as a combination of simple media feature tags.

   This document describes an abbreviated format for a composite media
   feature set, based upon a hash of the feature expression describing
   that composite.

Table of Contents

   1.    Introduction ................................................2
   1.1   Organization of this document ...............................2
   1.2   Terminology and document conventions ........................2
   2.    Motivation and goals ........................................3
   3.    Composite feature representation ............................4
   3.1   Feature set hashed reference format .........................5
   3.1.1 Hash value calculation ......................................6
   3.1.2 Base-32 value representation ................................7
   3.2   Resolving feature set identifiers ...........................8
   3.2.1 Query protocol ..............................................8
   3.2.2 Inline feature set details ..................................9
   4.    Examples ...................................................10
   5.    Internationalization Considerations ........................12
   6.    Security Considerations ....................................13
   7.    Acknowledgements ...........................................13
   8.    References .................................................13



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   9.    Authors' Addresses .........................................15
   10.   Appendix A: The birthday paradox ...........................16
   11.   Full Copyright Statement ...................................18

1. Introduction

   In "A Syntax for Describing Media Feature Sets" [1], an expression
   format is presented for describing media feature capabilities as a
   combination of simple media feature tags [2].

   This document proposes an abbreviated format for a composite media
   feature set, based upon a hash of the feature expression describing
   that composite.

   This memo extends and builds upon the expression syntax described in
   RFC 2533 [1], and it is assumed that the reader is familiar with the
   interpretation of feature set expressions described there.

1.1 Organization of this document

   Section 2 sets out some of the background and goals for feature set
   references.

   Section 3 presents a syntax for feature set references, and describes
   how they are related to feature set expressions.

1.2 Terminology and document conventions

   This section defines a number of terms and other document
   conventions, which are used with specific meaning in this memo.  The
   terms are listed in alphabetical order.

   dereference
            the act of replacing a feature set reference with its
            corresponding feature set expression.  Also called
            "resolution".

   feature set
            some set of media features described by a media feature
            assertion, as described in "A Syntax for Describing Media
            Feature Sets" [1].  (See that memo for a more formal
            definition of this term.)

   feature set expression
            a string that describes some feature set, formulated
            according to the rules in "A Syntax for Describing Media
            feature sets" [1] (and possibly extended by other
            specifications).



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   feature set reference
            a brief construct that references some feature set.  (See
            also: "dereference".)

   feature set tag
            a name that conforms to the syntax of a feature tag [2] that
            is used to denote a feature set rather than a single
            feature.

   resolution
            (See "dereference").

   This specification uses syntax notation and conventions described
   in RFC 2234, "Augmented BNF for Syntax Specifications: ABNF" [3].

       NOTE: Comments like this provide additional nonessential
       information about the rationale behind this document.  Such
       information is not needed for building a conformant
       implementation, but may help those who wish to understand the
       design in greater depth.

2. Motivation and goals

   The range of media feature capabilities of a message handling system
   can be quite extensive, and the corresponding feature set expression
   [1] can reach a significant size.

   A requirement has been identified to allow recurring feature sets to
   be identified by a single reference value, which can be combined with
   other elements in a feature set expression.  It is anticipated that
   mechanisms will be provided that allow the recipient of such a
   feature set reference to discover the corresponding feature set
   expression, but any such mechanism is beyond the scope of this
   specification.

   Thus, the goals for this proposal are:

   o  to provide an abbreviated form for referencing an arbitrary
      feature set expression.

   o  the meaning of (i.e., the corresponding feature set expression) a
      feature set reference should be independent of any particular
      mechanism that may be used to dereference it.

   o  to be able to verify whether a given feature set expression
      corresponds to some feature set reference without having to
      perform an explicit dereferencing operation (i.e., without
      incurring additional network traffic).



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   o  for protocol processors that conform to RFC 2533 [1] to be able to
      sensibly handle a feature set reference without explicit knowledge
      of its meaning (i.e., the introduction of feature set references
      should not break existing feature expression processors).  That
      is, the applicable interpretation and processing rules of RFC 2533
      [1] apply equally to expressions containing feature set
      references.

       NOTE:  This proposal does not attempt to address the "override"
       or "default" problem.  (Where a feature set may be referenced and
       selectively modified.)

   Some circumstances in which such an abbreviated form might be used
   include:

   o  A media feature expression that contains a repeated sub-
      expression.  If the sub-expression is quite large, space can be
      saved by writing it out once, then using the abbreviated form to
      reference it.

   o  A capability that is common to a range of devices, such as a given
      class of fax machine where are large number of feature tags are
      involved, but only a small number of common feature sets.  If the
      recipient understands, or can discover, that some abbreviation
      stands for a given feature set then feature expression size can be
      reduced by using the abbreviation.

      If feature set abbreviations are used in this way, it may be that
      they can be interpreted by a simple table lookup rather than full
      feature expression parsing.  (Making this useful in practice will
      depend on crafting the feature subsets appropriately.)

   Examples of such usage are given in section 4 of this memo.

   This memo does not specify how a program that receives a feature set
   abbreviation should discover the corresponding feature set
   expression: see section 3.2.

3. Composite feature representation

   This specification hinges on two central ideas:

   o  the use of auxiliary predicates (introduced in RFC 2533 [1]) to
      form the basis of a feature set identifier, and

   o  the use of a token based on a hash function computed over the
      referenced feature set expression.




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   A key reason to use a hash function to generate an identifier is to
   define a global name space without requiring a central naming
   authority.  New feature set tags can be introduced by any party
   following the appropriate rules of formulation, without reference to
   any centralized authority.

   Local resolution services may be needed to map feature set tags to
   their corresponding feature set expressions, but these are not able
   to vary the meaning of any given tag.  Failure of a resolution
   service to return the correct expression is detectable by a calling
   application, which should reject any incorrect value supplied.

       NOTE:  where a feature set reference is used, its meaning is
       defined by substitution of the referenced feature expression into
       the referencing expression.  When all references have been thus
       replaced, the result is interpreted as a normal feature
       expression.

       In particular, if a referenced feature expression contains some
       feature tag that is also constrained by the referencing
       expression, the constraints are interpreted per RFC 2533 [1],
       without regard for their origin.  E.g., (using some notation
       introduced below):
          (& (pix-x=100) (pix-y<=300)
             (h.SBB5REAOMHC09CP2GM4V07PQP0) )
       where (h.SBB5REAOMHC09CP2GM4V07PQP0) resolves to:
          (& (pix-x<=200) (pix-y<=150) )
       yields a result equivalent to:
          (& (pix-x=100) (pix-y<=150) )

3.1 Feature set hashed reference format

   This specification introduces a special form of auxiliary predicate
   name with the following syntax:

     fname       = "h." 1*BASE32DIGIT
     BASE32DIGIT = DIGIT
                 / "A" / "B" / "C" / "D" / "E" / "F" / "G" / "H"
                 / "I" / "J" / "K" / "L" / "M" / "N" / "O" / "P"
                 / "Q" / "R" / "S" / "T" / "U" / "V"

   The sequence of base-32 digits represents the value of a hash
   function calculated over the corresponding feature set expression
   (see following sections).  Note that the above syntax allows upper-
   or lower-case letters for base-32 digits (per RFC 2234 [3]).






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   Thus, within a feature set expression, a hashed feature set reference
   would have the following form:

      (h.123456789abcdefghijklmnopq)

3.1.1 Hash value calculation

   The hash value is calculated using the MD5 algorithm [6] over the
   text of the referenced feature set expression subjected to certain
   normalizations.  The feature expression must conform to the syntax
   given for 'filter' in RFC 2533 [1]:

      filter = "(" filtercomp ")" *( ";" parameter )

   The steps for calculating a hash value are:

   1. Whitespace normalization: all spaces, CR, LF, TAB and any other
      layout control characters that may be embedded in the feature
      expression string, other than those contained within quoted
      strings, are removed (or ignored for the purpose of hash value
      computation).

   2. Case normalization:  all lower case letters in the feature
      expression, other than those contained within quoted strings, are
      converted to upper case.  That is, unquoted characters with US-
      ASCII values 97 to 122 (decimal) are changed to corresponding
      characters in the range 65 to 90.

   3. Hash computation: the MD5 algorithm, described in RFC 1321 [6], is
      applied to the normalized feature expression string (represented
      as a sequence of octets containing US-ASCII character codes;  see
      also section 5).

      The result obtained in step 3 is a 128-bit (16 octet) value that
      is converted to a base-32 representation to form the feature set
      reference.

       NOTE:  under some circumstances, removal of ALL whitespace may
       result in an invalid feature expression string.  This should not
       be a problem as this is done only for the purpose of calculating
       a hash value, and significantly different feature expressions are
       expected to differ in ways other than their whitespace.

       NOTE: case normalization is deemed appropriate since feature tag
       and token matching is case insensitive.






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3.1.2 Base-32 value representation

   RFC 1321 [6] describes how to calculate an MD5 hash value that is a
   sequence of 16 octets.  This is then required to be coded as a base-
   32 value, which is a sequence of base-32 digit characters.

   Each successive character in a base-32 value represents 5 successive
   bits of the underlying octet sequence.  Thus, each group of 8
   characters represents a sequence of 5 octets (40 bits):

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

   The value (i.e. sequence of bits) represented by each base-32 digit
   character is indicated by the following table:

       "0"  0       "A"  10     "K"  20      "U"  30
       "1"  1       "B"  11     "L"  21      "V"  31
       "2"  2       "C"  12     "M"  22
       "3"  3       "D"  13     "N"  23
       "4"  4       "E"  14     "O"  24
       "5"  5       "F"  15     "P"  25
       "6"  6       "G"  16     "Q"  26
       "7"  7       "H"  17     "R"  27
       "8"  8       "I"  18     "S"  28
       "9"  9       "J"  19     "T"  29

   When encoding a base-32 value, each full group of 5 octets is
   represented by a sequence of 8 characters indicated above.  If a
   group of less than 5 octets remain after this, they are encoded using
   as many additional characters as may be needed:  1, 2, 3 or 4 octets
   are encoded by 2, 4, 5 or 7 characters respectively.  Any spare bits
   represented by the base-32 digit characters are selected to be zero.







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   When decoding a base-32 value, the reverse mapping is applied:  each
   full group of 8 characters codes a sequence of 5 octets.  A final
   group of 2, 4, 5 or 7 characters codes a sequence of 1, 2, 3 or 4
   octets respectively.  Any spare bits represented by the final group
   of characters are discarded.

   Thus, for a 128-bit (16 octet) MD5 hash value, the first 15 octets
   are coded as 24 base 32 digit characters, and the final octet is
   coded by two characters.

       NOTE:  Base64 representation (per MIME [4]) would be more compact
       (21 rather than 26 characters for the MD5 128-bit hash value),
       but an auxiliary predicate name is defined (by [1]) to have the
       same syntax as a feature tag, and the feature tag matching rules
       (per [2]) state that feature tag matching is case insensitive.

       Base36 representation was considered (i.e., using all letters
       "A"-"Z") but was not used because this would require extended
       precision multiplication and division operations to encode and
       decode the hash values.

3.2 Resolving feature set identifiers

   This memo does not mandate any particular mechanism for dereferencing
   a feature set identifier.  It is expected that specific dereferencing
   mechanisms will be specified for any application or protocol that
   uses them.

   The following sections describe some ways that feature set
   dereferencing information may be incorporated into a feature set
   expression.  These are based on auxiliary predicate definitions
   within a "where" clause [1].

   When a hashed feature set reference is used, conformance to the
   hashing rules takes precedence over any other determination of the
   feature expression.  Any expression, however obtained, may not be
   substituted for the hash-based reference unless it yields the correct
   hash value.

3.2.1 Query protocol

   A protocol providing request/response type queries (e.g., HTTP, LDAP,
   etc.) might be set up to provide a resolution service.

   Thus, a query to a server associated with the capabilities could be
   performed on the feature set identifier.  The response returned would
   be a CONNEG expression; e.g.,




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      (h.SBB5REAOMHC09CP2GM4V07PQP0)
      where
      (h.SBB5REAOMHC09CP2GM4V07PQP0) :- (& (pix-x<=200) (pix-y<=150) )
      end

   or just:

      (& (pix-x<=200) (pix-y<=150) )

   This result would be combined with the original expression to
   obtain a result not including the hash based predicate.

   This process might be further enhanced by using URN resolution
   mechanisms (e.g., DNS NAPTR [10]) to discover the resolution
   protocol and server.

3.2.2 Inline feature set details

   In this case, a reference is resolved by including its definition
   inline in an expression.

   The feature set expression associated with a reference value may be
   specified directly in a "where" clause, using the auxiliary
   predicate definition syntax [1]; e.g.,

      (& (dpi=100) (h.SBB5REAOMHC09CP2GM4V07PQP0) )
      where
      (h.SBB5REAOMHC09CP2GM4V07PQP0) :- (& (pix-x<=200) (pix-y<=150) )
      end

   This form might be used on request (where the request mechanism is
   defined by the invoking application protocol), or when the originator
   believes the recipient may not understand the reference.

   It is an error if the inline feature expression does not yield the
   hash value contained in auxiliary predicate name.

       NOTE:  viewed in isolation, this format does not have any obvious
       value, in that the (h.xxx) form of auxiliary predicate could be
       replaced by any arbitrary name.

       It is anticipated that this form might be used as a follow-up
       response in a sequence along the lines of:
          A> Capabilities are:
            (& (dpi=100) (h.SBB5REAOMHC09CP2GM4V07PQP0) )
          B> Do not understand:
            (h.SBB5REAOMHC09CP2GM4V07PQP0)




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          A> Capabilities are:
            (& (dpi=100) (h.SBB5REAOMHC09CP2GM4V07PQP0) )
            where
              (h.SBB5REAOMHC09CP2GM4V07PQP0) :- (& (pix-x<=200)
                (pix-y<=150) )
            end

4. Examples

   The following are some examples of feature set expressions containing
   feature set references:

      (& (dpi=100) (h.SBB5REAOMHC09CP2GM4V07PQP0) )

      (& (dpi=100) (h.SBB5REAOMHC09CP2GM4V07PQP0) )
      where
      (h.SBB5REAOMHC09CP2GM4V07PQP0) :-
        (& (pix-x<=200) (pix-y<=150) )
      end

      (h.QGEOPMCF02P09QC016CEPU22FO)
      where
      (h.QGEOPMCF02P09QC016CEPU22FO) :-
       (| (& (ua-media=continuous) (dpi=200) (dpi-xyratio=200/100)
             (color=Binary) (paper-size=B4) (image-coding=MH) )
          (& (ua-media=continuous) (dpi=200) (dpi-xyratio=200/100)
             (color=Binary) (paper-size=B4) (image-coding=MR) )
          (& (ua-media=stationery) (dpi=300) (dpi-xyratio=1)
             (color=Binary) (paper-size=A4) (image-coding=JBIG) )
          (& (ua-media=transparency) (dpi=300) (dpi-xyratio=1)

             (color=Binary) (paper-size=A4) (image-coding=JBIG) ) )
      end

   The following examples are based on Internet fax work, and show how a
   feature-hash might be used to express the commonly-used features.  A
   form of Internet fax system that is expected to be quite common is a
   so-called "simple mode" system, whose capabilities are described by
   the following feature expression:

      (& (image-file-structure=TIFF-minimal)
        (MRC-mode=0)
        (color=Binary)
        (image-coding=MH) (MRC-mode=0)
        (| (& (dpi=204) (dpi-xyratio=[204/98,204/196]) )
           (& (dpi=200) (dpi-xyratio=[200/100,1]) ) )
        (size-x<=2150/254)
        (paper-size=A4)



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        (ua-media=stationery) )

   This might be expressed by the hash-based feature set identifier:

      (h.MSB955PVIRT1QOHET9AJT5JM3O)

   The following example describes capabilities of a full-color
   Internet fax system.  Note a number of feature values are
   applicable in common with '(color=grey)' and '(color=full)':

      (& (image-file-structure=TIFF)
         (MRC-mode=0)
         (| (& (color=Binary)
               (image-coding=[MH,MR,MMR])
               (| (& (dpi=204) (dpi-xyratio=[204/98,204/196]) )
                  (& (dpi=200) (dpi-xyratio=[200/100,1]) )
                  (& (dpi=300) (dpi-xyratio=1) ) ) )
            (& (color=grey)
               (image-coding=JPEG)
               (image-coding-constraint=JPEG-T4E)
               (color-levels<=256)
               (color-space=CIELAB)
               (color-illuminant=D50)
               (CIELAB-L-min>=0)
               (CIELAB-L-max<=100)
               (dpi=[100,200,300]) (dpi-xyratio=1) )
            (& (color=full)
               (image-coding=JPEG)
               (image-coding-constraint=JPEG-T4E)
               (color-subsampling=["1:1:1","4:1:1"])
               (color-levels<=16777216)
               (color-space=CIELAB)
               (color-illuminant=D50)
               (CIELAB-L-min>=0)
               (CIELAB-L-max<=100)
               (CIELAB-a-min>=-85)
               (CIELAB-a-max<=85)
               (CIELAB-b-min>=-75)
               (CIELAB-b-max<=125)
               (dpi=[100,200,300]) (dpi-xyratio=1) ) )
         (size-x<=2150/254)
         (paper-size=[letter,A4,B4]) )
         (ua-media=stationery) )








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   Separating out the common capabilities yields:

     (& (image-file-structure=TIFF)
        (MRC-mode=0)
        (| (& (color=Binary)
              (image-coding=[MH,MR,MMR])
              (| (& (dpi=204) (dpi-xyratio=[204/98,204/196]) )
                 (& (dpi=200) (dpi-xyratio=[200/100,1]) )
                 (& (dpi=300) (dpi-xyratio=1) ) ) )
           (& (color=grey)
              (color-levels<=256)
              (h.QVSEM8V2LMJ8VOR7V682J7079O) )
           (& (color=full)
              (color-subsampling=["1:1:1","4:1:1"])
              (color-levels<=16777216)
              (CIELAB-a-min>=-85)
              (CIELAB-a-max<=85)
              (CIELAB-b-min>=-75)
              (CIELAB-b-max<=125)
              (h.QVSEM8V2LMJ8VOR7V682J7079O) ) )
        (size-x<=2150/254)
        (paper-size=[letter,A4,B4]) )
        (ua-media=stationery) )
     where
     (h.QVSEM8V2LMJ8VOR7V682J7079O) :-
        (& (image-coding=JPEG)
           (image-coding-constraint=JPEG-T4E)
           (color-space=CIELAB)
           (color-illuminant=D50)
           (CIELAB-L-min>=0)
           (CIELAB-L-max<=100)
           (dpi=[100,200,300]) (dpi-xyratio=1) )
     end

5. Internationalization Considerations

   Feature set expressions and URI strings are currently defined to
   consist of only characters from the US-ASCII repertoire [1,5]; under
   these circumstances this specification is not impacted by
   internationalization considerations (other than any already
   applicable to URIs [5]).

   But, if future revisions of the feature set syntax permit non-US-
   ASCII characters (e.g. within quoted strings), then some canonical
   representation must be defined for the purposes of calculating hash
   values.  One choice might be to use a UTF-8 equivalent representation
   as the basis for calculating the feature set hash.  Another choice




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   might be to leave this as an application protocol issue (but this
   could lead to non-interoperable feature sets between different
   protocols).

   Another conceivable issue is that of up-casing the feature expression
   in preparation for computing a hash value.  This does not apply to
   the content of strings so is not likely to be an issue.  But if
   changes are made that do permit non-US-ASCII characters in feature
   tags or token strings, consideration must be given to properly
   defining how case conversion is to be performed.

6. Security Considerations

   For the most part, security considerations are the same as those that
   apply for capability identification in general [1,2,9].

   A possible added consideration is that use of a specific feature set
   identifier may reveal more information about a system than is
   necessary for a transaction at hand.

7. Acknowledgements

   Ideas here have been improved by early discussions with Martin
   Duerst, Al Gilman and Ted Hardie.  Useful suggestions for improvement
   were provided by Maurizio Codogno.

8. References

   [1]  Klyne, G., "A Syntax for Describing Media Feature Sets", RFC
        2533, March 1999.

   [2]  Mutz, A. and T. Hardie, "Media Feature Tag Registration
        Procedure", RFC 2506, March 1999.

   [3]  Crocker, D. and P. Overell, "Augmented BNF for Syntax
        Specifications: ABNF", RFC 2234, November 1997.

   [4]  Freed, N. and N. Borenstein,  "Multipurpose Internet Mail
        Extensions (MIME) Part 1: Format of Internet message bodies",
        RFC 2045, November 1996.

   [5]  Berners-Lee, T., Fielding, R. and L. Masinter, "Uniform Resource
        Identifiers (URI): Generic Syntax", RFC 2396, August 1998.

   [6]  Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321, April
        1992.





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   [7]  "Applied Cryptography"
        Bruce Schneier
        John Wiley and Sons, 1996 (second edition)
        ISBN 0-471-12845-7 (cloth)
        ISBN 0-471-11709-9 (paper)

   [8]  Klyne, G., "Protocol-independent Content Negotiation Framework",
        RFC 2703, September 1999.

   [9]  "Numerical Recipes"
        William H Press, Brian P Flannery, Saul A Teukolski and
        William T Vetterling
        Cambridge University Press (1986)
        ISBN 0 521 30811 9
        (The Gamma function approximation is presented in chapter 6 on
        "Special Functions".  There have been several later editions of
        this book published, so the chapter reference may change.)

   [10] Daniel, R. and M. Mealling, "Resolution of Uniform Resource
        Identifiers using the Domain Name System", RFC 2168, June 1997.

   [11] Java source code of feature set matching algorithm, with feature
        set hash computation option.  Linked from
        <http://www.imc.org/ietf-medfree/>



























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9. Authors' Addresses

   Graham Klyne
   Content Technologies Ltd.
   1220 Parkview,
   Arlington Business Park
   Theale
   Reading, RG7 4SA
   United Kingdom

   Phone: +44 118 930 1300
   Fax:   +44 118 930 1301
   EMail: GK@ACM.ORG


   Larry Masinter
   AT&T Labs
   75 Willow Road
   Menlo Park, CA 94025

   Phone: +1-650-463-7059
   EMail: LMM@acm.org
   http://larry.masinter.net




























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10. Appendix A: The birthday paradox

       NOTE: this entire section is commentary, and does not affect the
       feature set reference specification in any way.

   The use of a hash value to represent an arbitrary feature set is
   based on a presumption that no two distinct feature sets will yield
   the same hash value.

   There is a small but distinct possibility that two different feature
   sets will indeed yield the same hash value.

   We assume that the 128-bit hash function distributes hash values for
   feature sets, even those with very small differences, randomly and
   evenly through the range of 2^128 (approximately 3*10^38) possible
   values.  This is a fundamental property of a good digest algorithm
   like MD5.  Thus, the chance that any two distinct feature set
   expressions yield the same hash is less than 1 in 10^38.  This is
   negligible when compared with, say, the probability that a receiving
   system will fail having received data conforming to a negotiated
   feature set.

   But when the number of distinct feature sets in circulation
   increases, the probability of repeating a hash value increases
   surprisingly.  This is illustrated by the "birthday paradox":  given
   a random collection of just 23 people, there is a greater than even
   chance that there exists some pair with the same birthday.  This
   topic is discussed further in sections 7.4 and 7.5 of Bruce
   Schneier's "Applied Cryptography" [7].

   The table below shows the "birthday paradox" probabilities that at
   least one pair of feature sets has the same hash value for different
   numbers of feature sets in use.

          Number of feature   Probability of two
          sets in use         sets with the same
                              hash value
          1                   0
          2                   3E-39
          10                  1E-37
          1E3                 1E-33
          1E6                 1E-27
          1E9                 1E-21
          1E12                1E-15
          1E15                1E-9
          1E18                1E-3





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       The above probability computations are approximate, being
       performed using logarithms of a Gamma function
       approximation by Lanczos [9].  The probability formula is
       'P=1-(m!/((m-n)! m^n))', where 'm' is the total number of
       possible hash values (2^128) and 'n' is the number of
       feature sets in use.

   If original feature set expressions are generated manually, or only
   in response to some manually constrained process, the total number
   of feature sets in circulation is likely to remain very small in
   relation to the total number of possible hash values.

   The outcome of all this is: assuming that the feature sets are
   manually generated, even taking account of the birthday paradox
   effect, the probability of incorrectly identifying a feature set
   using a hash value is still negligibly small when compared with
   other possible failure modes.


































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11.  Full Copyright Statement

   Copyright (C) The Internet Society (2000).  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 assigns.

   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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