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 fins00013) 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 15You 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 NA 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 30959For 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 0.78916761796439427457bits 10 number 1024:
6 0.98543241551841020964 7 0.97965839745873206645 11 0.94753115178840541244 16 0.88888866335604777014 22 0.79677613655632184564bits 11 number 2048:
7 0.98978773152834598203 10 0.97823367137821537476 15 0.94990722378677450166 22 0.89298119682681720288 31 0.79597589885472519455bits 12 number 4096:
10 0.98906539062491305447 14 0.97800426773009718762 21 0.94994111694430838355 30 0.89901365764115603874 44 0.79312138620093930452bits 13 number 8192:
14 0.98894703242829806733 19 0.97932692503837115439 30 0.94822407309193512681 43 0.89545741661906652631 61 0.7993625840767998314bits 14 number 16384:
19 0.98961337517641645434 27 0.97879319536756481668 42 0.94876352395820107155 60 0.89748107890372830209 86 0.79973683158771624591bits 15 number 32768:
27 0.98934263776790121181 37 0.97987304880641035165 59 0.94909471808051404373 84 0.89899774209805793923 122 0.79809378598190949816bits 16 number 65536:
37 0.98988724065590050216 52 0.97996496661944154649 83 0.94937874420413270737 118 0.89996948010355670711 172 0.79884228150816105618bits 17 number 131072:
52 0.98993311138884398925 74 0.97960010416289267088 117 0.94952974978505377823 167 0.89960828942716541956 243 0.79894309171178368167bits 18 number 262144:
74 0.98974844864797828503 104 0.97977315557223210174 165 0.94968621078621640041 236 0.8995926348279144058 343 0.7994422793765953994bits 19 number 524288:
104 0.98983557888923057178 147 0.97973841652874515962 233 0.94974719445364064185 333 0.89991342619657743729 485 0.79936749144148444568bits 20 number 1048576:
146 0.98995567500195758015 207 0.97987072919607220989 329 0.94983990872655321702 471 0.89980857451706741656 685 0.79974215234216872172bits 21 number 2097152:
206 0.98998177463778547214 292 0.97994400939715686771 465 0.94985589918092261374 666 0.89978055267663470396 968 0.79994886751736571373bits 22 number 4194304:
291 0.98999013137747737812 413 0.97991951242142538714 657 0.94991674892578203959 941 0.89991652739633254399 1369 0.79989205747440361716bits 23 number 8388608:
412 0.98995762604049764022 583 0.97997846530691334888 929 0.94991024716640248826 1330 0.89999961063320443877 1936 0.79987028265451087794bits 24 number 16777216:
582 0.98997307486745211857 824 0.97999203469417239809 1313 0.94995516684099989835 1881 0.89997049960675035152 2737 0.79996700222056416063bits 25 number 33554432:
822 0.98999408609360783906 1165 0.9799956928177964155 1856 0.9499899669674316538 2660 0.8999664414095410736 3871 0.79992328289672998132bits 26 number 67108864:
1162 0.98999884535478044345 1648 0.9799801637652703068 2625 0.94997437525354821997 3761 0.89999748465616635773 5474 0.79993922903192515861bits 27 number 134217728:
1644 0.9899880636014986024 2330 0.97998730103356856969 3712 0.94997727934463771504 5319 0.89998552434244594167 7740 0.79999591580103557309bits 28 number 268435456:
2324 0.98999458855588851058 3294 0.97999828329325222587 5249 0.94998397932368705554 7522 0.89998576049206902017 10946 0.79999058777500076101bits 29 number 536870912:
3286 0.98999717306002099626 4659 0.97999160965267329004 7422 0.94999720388831232487 10637 0.89999506567702891591 15480 0.7999860979665908145bits 30 number 1073741824:
4647 0.98999674474047760775 6588 0.97999531736215383937 10496 0.94999806770951356061 15043 0.89999250738244507275 21891 0.79999995570982085358bits 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 55455-0134EMail: Craig.A.Finseth-1@umn.edu or fin@unet.umn.eduPhone: +1 612 624 3375
Fax: +1 612 626 1002