ALGORITHM

The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, National Provider Identification Number in US and Canadian Social Insurance Numbers. It was created by IBM scientist Hans Peter Luhn and described in U.S. Patent 2,950,048, filed on January 6, 1954, and granted on August 23, 1960.

The algorithm is in the public domain and is in wide use today. It is specifed in ISO/IEC 7812-1. It is not intended to be a cryptographically secure hash function; it was designed to protect against accidental errors, not malicious attacks. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from collections of random digits.The Luhn algorithm will detect any single-digit error, as well as almost all transpositions of adjacent digits. It will not, however, detect transposition of the two-digit sequence 09 to 90 (or vice versa). It will detect 7 of the 10 possible twin errors (it will not detect 22 ↔ 55, 33 ↔ 66 or 44 ↔ 77).

Other, more complex check-digit algorithms (such as the Verhoeff algorithm) can detect more transcription errors. The Luhn 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 only affect the result if they cause shift in position, zero-padding the beginning of a string of numbers does not affect the calculation. Therefore, systems that normalize to a specific number of digits by converting 1234 to 00001234 (for instance) can perform Luhn validation before or after the normalization and achieve the same result.

The algorithm appeared in a US Patent for a hand-held, mechanical device for computing the checksum. It was therefore required to be rather simple. The device took the mod 10 sum by mechanical means. The substitution 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.