Hawkynt

Luhn

Luhn algorithm (mod 10 algorithm) for validating identification numbers. Invented by Hans Peter Luhn at IBM in 1954. Used in credit cards, IMEI, Canadian SIN. Detects all single-digit errors and most adjacent transpositions.

Properties

Property	Value
Category	Checksums
Sub-category	Check Digit
Security status	🎓 Educational Only
Complexity	Beginner
Inventor	Hans Peter Luhn (IBM)
Year	1954
Origin	🇺🇸 United States
Source	`algorithms/checksum/luhn.js`

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Notes

Algorithm: From right to left, double every second digit
If doubled digit > 9, subtract 9 (equivalent to adding digits: 16→1+6=7)
Sum all digits, check digit = (10 - sum % 10) % 10
Validation: sum of all digits including check digit ≡ 0 (mod 10)
Detects: All single-digit errors
Detects: Most (but not all) adjacent transpositions
Used in: Visa, MasterCard, American Express, IMEI numbers
Not cryptographically secure - only for error detection

Documentation

References

python-stdnum Luhn implementation

Test vectors

3 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Rosetta Code test vector 49927398716

Field	Value
`input`	`34393932373339383731`
`expected`	`06`

Vector 2 — Rosetta Code test vector 1234567812345670

Field	Value
`input`	`313233343536373831323334353637`
`expected`	`00`

Vector 3 — Simple Luhn test 12345674

Field	Value
`input`	`31323334353637`
`expected`	`04`

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