TheLuhn algorithm orLuhn formula (creator:IBM scientistHans Peter Luhn), also known as the "modulus 10" or "mod 10"algorithm, is a simplecheck digit formula used to validate a variety of identification numbers.[a] The purpose is to design a numbering scheme in such a way that when a human is entering a number, a computer can quickly check it for errors.
The algorithm is in thepublic domain and is in wide use today. It is specified inISO/IEC 7812-1.[2] It is not intended to be acryptographically secure hash function; it was designed to protect against accidental errors, not malicious attacks. Mostcredit card numbers and manygovernment identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers.
The check digit is computed as follows:
Assume an example of an account number 1789372997 (just the "payload", check digit not yet included):
| Digits reversed | 7 | 9 | 9 | 2 | 7 | 3 | 9 | 8 | 7 | 1 |
|---|---|---|---|---|---|---|---|---|---|---|
| Multipliers | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 |
| = | = | = | = | = | = | = | = | = | = | |
| 14 | 9 | 18 | 2 | 14 | 3 | 18 | 8 | 14 | 1 | |
| Sum digits | 5 (1+4) | 9 | 9 (1+8) | 2 | 5 (1+4) | 3 | 9 (1+8) | 8 | 5 (1+4) | 1 |
The sum of the resulting digits is 56.
The check digit is equal to.
This makes the full account number read 17893729974.
The Luhn algorithm will detect all single-digit errors, as well as almost all transpositions of adjacent digits. It will not, however, detect transposition of the two-digit sequence09 to90 (or vice versa). It will detect most of the possible twin errors (it will not detect22 ↔55,33 ↔66 or44 ↔77).
Other, more complex check-digit algorithms (such as theVerhoeff algorithm and theDamm algorithm) can detect more transcription errors. TheLuhn mod N algorithm is an extension that supports non-numerical strings.
Because the algorithm operates on the digits in a right-to-left manner and zero digits affect the result only if they cause shift in position, zero-padding the beginning of a string of numbers does not affect the calculation. Therefore, systems that pad to a specific number of digits (by converting 1234 to 0001234 for instance) can perform Luhn validation before or after the padding and achieve the same result.
The algorithm appeared in a United States Patent[1] for a simple, hand-held, mechanical device for computing the checksum. The device took the mod 10 sum by mechanical means. Thesubstitution digits, that is, the results of the double and reduce procedure, were not produced mechanically. Rather, the digits were marked in their permuted order on the body of the machine.
The following function takes a card number, including the check digit, as an array of integers and outputstrue if the check digit is correct,false otherwise.
function isValid(cardNumber[1..length]) sum := 0 parity := length mod 2for i from 1 to (length - 1)doif i mod 2 == paritythen sum := sum + cardNumber[i]elseif cardNumber[i] > 4then sum := sum + 2 * cardNumber[i] - 9else sum := sum + 2 * cardNumber[i]end ifend forreturn cardNumber[length] == ((10 - (sum mod 10)) mod 10)end function
The Luhn algorithm is used in a variety of systems, including:
