RFC1439

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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.

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.

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.

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

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

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

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

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

  1. !/usr/local/bin/perl

for $bits (6..31) {

       &Compute($bits);
       }

exit(0);

  1. ------------------------------------------------------------

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: [email protected] or

      [email protected]

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