Luhnregel

Luhnregel, also known as the Luhn algorithm, is a simple checksum method used to validate identification numbers that include a check digit. It was devised by Hans Peter Luhn of IBM in 1954. The goal is to detect common input errors, such as a single incorrect digit or adjacent-digit transposition, in long numeric identifiers used in finance and telecommunications.

The algorithm works by processing the digits from right to left. Starting with the second digit from the right, every other digit is doubled. If doubling yields a number greater than 9, 9 is subtracted from it. All digits, after this transformation, are summed together with the check digit. A number is valid under the Luhn rule if the total is a multiple of 10.

As an illustration, the number 79927398713 is valid under the Luhn check; applying the steps described above produces a total sum that ends in 0, fulfilling the mod 10 criterion.

The Luhnregel is widely used as a check digit in credit and debit card numbers, as well as in other identifiers such as IMEI mobile device IDs and certain national identification numbers, including the Canadian Social Insurance Number. It remains a practical, lightweight validation tool in many systems.

Limitations include that the method is not cryptographically secure and does not protect against deliberate forgery. It is designed to detect accidental errors and a large proportion of typographical mistakes, but not all possible errors or sophisticated fraud. Some systems use variations or additional checks alongside Luhn.