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Verhoeff

Verhoeff algorithm using dihedral group D5 for superior error detection. Detects ALL single-digit errors and ALL adjacent transposition errors, unlike Luhn. Invented by Dutch mathematician Jacobus Verhoeff in 1969.

Properties

Property	Value
Category	Checksums
Sub-category	Check Digit
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Jacobus Verhoeff
Year	1969
Origin	🇳🇱 Netherlands
Source	`algorithms/checksum/verhoeff.js`

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Notes

Uses three mathematical tables: multiplication, permutation, inverse
Based on dihedral group D5 (symmetries of pentagon)
Detects: 100% of single-digit errors
Detects: 100% of adjacent transposition errors
Detects: 95.3% of twin errors (e.g., 22→33)
Detects: 94.2% of jump transpositions (e.g., abc→cba)
Superior to Luhn but more complex
Used in: German Betriebsnummer, SIM card serial numbers

Documentation

References

python-stdnum Verhoeff 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 236

Field	Value
`input`	`323336`
`expected`	`03`

Vector 2 — Rosetta Code test vector 12345

Field	Value
`input`	`3132333435`
`expected`	`01`

Vector 3 — Rosetta Code test vector 123456789012

Field	Value
`input`	`313233343536373839303132`
`expected`	`00`

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