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RFC 1439 - The Uniqueness of Unique Identifiers


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Network Working Group                                         C. Finseth
Request for Comments: 1439                       University of Minnesota
                                                              March 1993

                  The Uniqueness of Unique Identifiers

Status of this Memo

   This memo provides information for the Internet community.  It does
   not specify an Internet standard.  Distribution of this memo is
   unlimited.

Abstract

   This RFC provides information that may be useful when selecting a
   method to use for assigning unique identifiers to people.

1. The Issue

   Computer systems require a way to identify the people associated with
   them.  These identifiers have been called "user names" or "account
   names."  The identifers are typically short, alphanumeric strings.
   In general, these identifiers must be unique.

   The uniqueness is usually achieved in one of three ways:

   1) The identifiers are assigned in a unique manner without using
   information associated with the individual.  Example identifiers are:

           ax54tv
           cs00034

   This method was often used by large timesharing systems.  While it
   achieved the uniqueness property, there was no way of guessing the
   identifier without knowing it through other means.

   2) The identifiers are assigned in a unique manner where the bulk of
   the identifier is algorithmically derived from the individual's name.
   Example identifers are:

           Craig.A.Finseth-1
           Finseth1
           caf-1
           fins0001

   3) The identifiers are in general not assigned in a unique manner:
   the identifier is algorithmically derived from the individual's name

   and duplicates are handled in an ad-hoc manner.  Example identifiers
   are:

           Craig.Finseth
           caf

   Now that we have widespread electronic mail, an important feature of
   an identifier system is the ability to predict the identifier based
   on other information associated with the individual.  This other
   information is typically the person's name.

   Methods two and three make such predictions possible, especially if
   you have one example mapping from a person's name to the identifier.
   Method two relies on using some or all of the name and
   algorithmically varying it to ensure uniqueness (for example, by
   appending an integer).  Method three relies on using some or all of
   the name and selects an alternate identifier in the case of a
   duplication.

   For both methods, it is important to minimize the need for making the
   adjustments required to ensure uniqueness (i.e., an integer that is
   not 1 or an alternate identifier).  The probability that an
   adjustment will be required depends on the format of the identifer
   and the size of the organization.

2. Identifier Formats

   There are a number of popular identifier formats.  This section will
   list some of them and supply both typical and maximum values for the
   number of possible identifiers.  A "typical" value is the number that
   you are likely to run into in real life.  A "maximum" value is the
   largest number of possible (without getting extreme about it) values.
   All ranges are expressed as a number of bits.

2.1 Initials

   There are three popular formats based on initials: those with one,
   two, or three letters.  (The number of people with more than three
   initials is assumed to be small.)  Values:

           format                  typical         maximum

           I                       4               5
           II                      8               10
           III                     12              15

   You can also think of these as first, middle, and last initials:

           I                       4               5
           F L                     8               10
           F M L                   12              15

2.2 Names

   Again, there are three popular formats based on using names: those
   with the first name, last name, and both first and last names.
   Values:

           format                  typical         maximum

           First                   8               14
           Last                    9               13
           First Last              17              27

2.3 Combinations

   I have seen these combinations in use ("F" is first initial, "M" is
   middle initial, and "L" is last initial):

           format                  typical         maximum

           F Last                  13              18
           F M Last                17              23
           First L                 12              19
           First M Last            21              32

2.4 Complete List

   Here are all possible combinations of nothing, initial, and full name
   for first, middle, and last.  The number of Middle names is assumed
   to be the same as the number of First names.  Values:

           format                  typical         maximum

           _ _ _                   0               0
           _ _ L                   4               5
           _ _ Last                9               13

           _ M _                   4               5
           _ M L                   5               10
           _ M Last                13              18

           _ Middle _              8               14
           _ Middle L              12              19

           _ Middle Last           17              27

           F _ _                   4               5
           F _ L                   5               10
           F _ Last                13              18

           F M _                   5               10
           F M L                   12              15
           F M Last                17              23

           F Middle _              12              19
           F Middle L              16              24
           F Middle Last           21              32

           First _ _               8               14
           First _ L               12              19
           First _ Last            17              27

           First M _               12              19
           First M L               16              24
           First M Last            21              32

           First Middle _          16              28
           First Middle L          20              33
           First Middle Last       26              40

3. Probabilities of Duplicates

   As can be seen, the information content in these identifiers in no
   case exceeds 40 bits and the typical information content never
   exceeds 26 bits.  The content of most of them is in the 8 to 20 bit
   range.  Duplicates are thus not only possible but likely.

   The method used to compute the probability of duplicates is the same
   as that of the well-known "birthday" problem.  For a universe of N
   items, the probability of duplicates in X members is expressed by:

           N   N-1   N-2         N-(X-1)
           - x --- x --- x ... x -------
           N    N     N             N

   A program to compute this function for selected values of N is given
   in the appendix, as is its complete output.

   The "1%" column is the number of items (people) before an
   organization of that (universe) size has a 1% chance of a duplicate.
   Similarly for 2%, 5%, 10%, and 20%.

           bits       universe     1%      2%      5%      10%     20%

            6                 64   2       3       4       5       6
            7                128   3       3       5       6       8
            8                256   3       4       6       8       12
            9                512   4       6       8       11      16
           10              1,024   6       7       11      16      22
           11              2,048   7       10      15      22      31
           12              4,096   10      14      21      30      44
           13              8,192   14      19      30      43      61
           14             16,384   19      27      42      60      86
           15             32,768   27      37      59      84      122
           16             65,536   37      52      83      118     172
           17            131,072   52      74      117     167     243
           18            262,144   74      104     165     236     343
           19            524,288   104     147     233     333     485
           20          1,048,576   146     207     329     471     685
           21          2,097,152   206     292     465     666     968
           22          4,194,304   291     413     657     941     1369
           23          8,388,608   412     583     929     1330    1936
           24         16,777,216   582     824     1313    1881    2737
           25         33,554,432   822     1165    1856    2660    3871
           26         67,108,864   1162    1648    2625    3761    5474
           27        134,217,728   1644    2330    3712    5319    7740
           28        268,435,456   2324    3294    5249    7522    10946
           29        536,870,912   3286    4659    7422    10637   15480
           30      1,073,741,824   4647    6588    10496   15043   21891
           31      2,147,483,648   6571    9316    14844   21273   30959

   For example, assume an organization were to select the "First Last"
   form.  This form has 17 bits (typical) and 27 bits (maximum) of
   information.  The relevant line is:

           17            131,072   52      74      117     167     243

   For an organization with 100 people, the probability of a duplicate
   would be between 2% and 5% (probably around 4%).  If the organization
   had 1,000 people, the probability of a duplicate would be much
   greater than 20%.

Appendix: Reuse of Identifiers and Privacy Issues

   Let's say that an organization were to select the format:

           First.M.Last-#

   as my own organization has.  Is the -# required, or can one simply
   do:

           Craig.A.Finseth

   for the first one and

           Craig.A.Finseth-2

   (or -1) for the second?  The answer is "no," although for non-obvious
   reasons.

   Assume that the organization has made this selection and a third
   party wants to send e-mail to Craig.A.Finseth.  Because of the
   Electronic Communications Privacy Act of 1987, an organization must
   treat electronic mail with care.  In this case, there is no way for
   the third party user to reliably know that sending to Craig.A.Finseth
   is (may be) the wrong party.  On the other hand, if the -# suffix is
   always present and attempts to send mail to the non-suffix form are
   rejected, the third party user will realize that they must have the
   suffix in order to have a unique identifier.

   For similar reasons, identifiers in this form should not be re-used
   in the life of the mail system.

Appendix: Perl Program to Compute Probabilities

   #!/usr/local/bin/perl

   for $bits (6..31) {
           &Compute($bits);
           }
   exit(0);

   # ------------------------------------------------------------

   sub Compute {
           $bits = $_[0];
           $num = 1 << $bits;
           $cnt = $num;

           print "bits $bitsnumber $num:0;

           for ($prob = 1; $prob > 0.99; ) {
                   $prob *= $cnt / $num;
                   $cnt--;
                   }

           print "", $num - $cnt, "$prob0;

           for (; $prob > 0.98; ) {

                   $prob *= $cnt / $num;
                   $cnt--;
                   }
           print "", $num - $cnt, "$prob0;

           for (; $prob > 0.95; ) {
                   $prob *= $cnt / $num;
                   $cnt--;
                   }
           print "", $num - $cnt, "$prob0;

           for (; $prob > 0.90; ) {
                   $prob *= $cnt / $num;
                   $cnt--;
                   }
           print "", $num - $cnt, "$prob0;

           for (; $prob > 0.80; ) {
                   $prob *= $cnt / $num;
                   $cnt--;
                   }
           print "", $num - $cnt, "$prob0;

           print "0;
           }

Appendix: Perl Program Output

   bits 6  number 64:
           2       0.984375
           3       0.95361328125
           4       0.90891265869140625
           5       0.85210561752319335938
           6       0.78553486615419387817

   bits 7  number 128:
           3       0.9766845703125
           3       0.9766845703125
           5       0.92398747801780700684
           6       0.88789421715773642063
           8       0.79999355674331695809

   bits 8  number 256:
           3       0.988311767578125
           4       0.97672998905181884766
           6       0.94268989971169503406
           8       0.89542306910786462204
           12      0.76969425214152431547

   bits 9  number 512:
           4       0.98832316696643829346
           6       0.97102570187075798458
           8       0.94652632751096643648
           11      0.89748056780293572476
           16      0.78916761796439427457

   bits 10 number 1024:
           6       0.98543241551841020964
           7       0.97965839745873206645
           11      0.94753115178840541244
           16      0.88888866335604777014
           22      0.79677613655632184564

   bits 11 number 2048:
           7       0.98978773152834598203
           10      0.97823367137821537476
           15      0.94990722378677450166
           22      0.89298119682681720288
           31      0.79597589885472519455

   bits 12 number 4096:
           10      0.98906539062491305447
           14      0.97800426773009718762
           21      0.94994111694430838355
           30      0.89901365764115603874
           44      0.79312138620093930452

   bits 13 number 8192:
           14      0.98894703242829806733
           19      0.97932692503837115439
           30      0.94822407309193512681
           43      0.89545741661906652631
           61      0.7993625840767998314

   bits 14 number 16384:
           19      0.98961337517641645434
           27      0.97879319536756481668
           42      0.94876352395820107155
           60      0.89748107890372830209
           86      0.79973683158771624591

   bits 15 number 32768:
           27      0.98934263776790121181
           37      0.97987304880641035165
           59      0.94909471808051404373
           84      0.89899774209805793923
           122     0.79809378598190949816

   bits 16 number 65536:
           37      0.98988724065590050216
           52      0.97996496661944154649
           83      0.94937874420413270737
           118     0.89996948010355670711
           172     0.79884228150816105618

   bits 17 number 131072:
           52      0.98993311138884398925
           74      0.97960010416289267088
           117     0.94952974978505377823
           167     0.89960828942716541956
           243     0.79894309171178368167

   bits 18 number 262144:
           74      0.98974844864797828503
           104     0.97977315557223210174
           165     0.94968621078621640041
           236     0.8995926348279144058
           343     0.7994422793765953994

   bits 19 number 524288:
           104     0.98983557888923057178
           147     0.97973841652874515962
           233     0.94974719445364064185
           333     0.89991342619657743729
           485     0.79936749144148444568

   bits 20 number 1048576:
           146     0.98995567500195758015
           207     0.97987072919607220989
           329     0.94983990872655321702
           471     0.89980857451706741656
           685     0.79974215234216872172

   bits 21 number 2097152:
           206     0.98998177463778547214
           292     0.97994400939715686771
           465     0.94985589918092261374
           666     0.89978055267663470396
           968     0.79994886751736571373

   bits 22 number 4194304:
           291     0.98999013137747737812
           413     0.97991951242142538714
           657     0.94991674892578203959
           941     0.89991652739633254399
           1369    0.79989205747440361716

   bits 23 number 8388608:
           412     0.98995762604049764022
           583     0.97997846530691334888
           929     0.94991024716640248826
           1330    0.89999961063320443877
           1936    0.79987028265451087794

   bits 24 number 16777216:
           582     0.98997307486745211857
           824     0.97999203469417239809
           1313    0.94995516684099989835
           1881    0.89997049960675035152
           2737    0.79996700222056416063

   bits 25 number 33554432:
           822     0.98999408609360783906
           1165    0.9799956928177964155
           1856    0.9499899669674316538
           2660    0.8999664414095410736
           3871    0.79992328289672998132

   bits 26 number 67108864:
           1162    0.98999884535478044345
           1648    0.9799801637652703068
           2625    0.94997437525354821997
           3761    0.89999748465616635773
           5474    0.79993922903192515861

   bits 27 number 134217728:
           1644    0.9899880636014986024
           2330    0.97998730103356856969
           3712    0.94997727934463771504
           5319    0.89998552434244594167
           7740    0.79999591580103557309

   bits 28 number 268435456:
           2324    0.98999458855588851058
           3294    0.97999828329325222587
           5249    0.94998397932368705554
           7522    0.89998576049206902017
           10946   0.79999058777500076101

   bits 29 number 536870912:
           3286    0.98999717306002099626
           4659    0.97999160965267329004
           7422    0.94999720388831232487
           10637   0.89999506567702891591
           15480   0.7999860979665908145

   bits 30 number 1073741824:
           4647    0.98999674474047760775
           6588    0.97999531736215383937
           10496   0.94999806770951356061
           15043   0.89999250738244507275
           21891   0.79999995570982085358

   bits 31 number 2147483648:
           6571    0.98999869761078929109
           9316    0.97999801528523688976
           14844   0.94999403283519279206
           21273   0.89999983631135749285
           30959   0.79999272222201334159

References

   Bruce Lansky (1984).  The Best Baby Name Book.  Deephaven, MN:
   Meadowbrook.  ISBN 0-671-54463-2.

   Lareina Rule (1988).  Name Your Baby.  Bantam.  ISBN 0-553-27145-8.

Security Considerations

   Security issues are not discussed in this memo.

Author's  Address

   Craig A. Finseth
   Networking Services
   Computer and Information Services
   University of Minnesota
   130 Lind Hall
   207 Church St. SE
   Minneapolis, MN 55455-0134

   EMail: Craig.A.Finseth-1@umn.edu or
          fin@unet.umn.edu

   Phone: +1 612 624 3375
   Fax: +1 612 626 1002

 

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