Luhn algorithm: Difference between revisions

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{{Short description|Simple checksum formula}}

{{redirects|Luhn|people named Luhn|Luhn (surname)}}

The '''Luhn algorithm''' or '''Luhn formula''' (creator: [[IBM]] scientist [[Hans Peter Luhn]]), also known as the "[[modular arithmetic|modulus]] 10" or "mod 10" [[algorithm]], named after its creator, [[IBM]] scientist [[Hans Peter Luhn]], is a simple [[check digit]] formula used to validate a variety of identification numbers. {{efn|It is described in [[United States|US]] patent 2950048A, granted on {{date|1960-08-23|DMY}}.<ref name="US2950048A">{{cite patent|title=Computer for Verifying Numbers|country=US|number=2950048A|status=patent|pubdate={{date|1960-08-23|DMY}}|gdate={{date|1960-08-23|DMY}}|invent1=Luhn|inventor1-first=Hans Peter|fdate=1954-01-06|inventorlink=Hans Peter Luhn}}</ref>}}

The algorithm is in the [[public ___domain]] and is in wide use today. It is specified in [[ISO/IEC 7812-1]].<ref>{{cite tech report|title=Identification cards {{mdash}} Identification of issuers {{mdash}} Part 1: Numbering system|number=[[ISO/IEC 7812]]-1:{{date|2017|DMY}}|institution=[[International Organization for Standardization]] & [[International Electrotechnical Commission]]|date={{date|Jan 2017|DMY}}|type=standard|url=https://www.iso.org/standard/70484.html|chapter=Annex B: Luhn formula for computing modulus-10 “double-add-double” check digits}}</ref> It is not intended to be a [[cryptographic hash function|cryptographically secure hash function]]; it was designed to protect against accidental errors, not malicious attacks. Most [[credit card number]]s and many [[government identification numbers]] use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers.

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Assume an example of an account number 1789372997 (just the "payload", check digit not yet included):

{| class="wikitable" style="text-align:center;border:none;background:transparent;"

|! style="width:1.5em" | Digits reversed

| style="width:1.5em" | 7

| style="width:1.5em" | 9

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|-

!

| style="background: #FFA; color: #000;" | '''14'''

| 9

| style="background: #FFA; color: #000;" | '''18'''

| 2

| style="background: #FFA; color: #000;" | '''14'''

| 3

| style="background: #FFA; color: #000;" | '''18'''

| 8

| style="background: #FFA; color: #000;" | '''14'''

| 1

|-

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parity := length mod 2

'''for''' i from 1 to (length - 1) '''do'''

'''if''' i mod 2 !== parity '''then'''

sum := sum + cardNumber[i]

'''elseif''' cardNumber[i] > 4 '''then'''

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* [[South Africa|South African]] ID numbers

* [[South Africa|South African]] Tax reference numbers

* [[Personal identity number (Sweden)| Swedish]] [[nationalPersonal identificationidentity numbers number]]s

* [[Sweden|Swedish]] Corporate Identity Numbers (OrgNr)

* [[Greece|Greek]] Social Security Numbers (ΑΜΚΑ)

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==References==

<references/>

==Notes==

{{notelist}}

==External links==

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[[Category:1954 introductions]]

[[Category:Articles with example pseudocode]]

[[Category:Management cybernetics]]