Modulo10menetelmä

Modulo10menetelmä, also known as the modulo 10 method or the Luhn algorithm, is a checksum formula used to validate numbers that include a check digit. It is widely used in identifiers such as credit and debit card numbers, as well as other identifying sequences, to detect common transcription errors.

How it works in brief: starting from the rightmost digit and moving left, every second digit is doubled. If doubling yields a number greater than 9, 9 is subtracted from the result (equivalently, the digits of the product are summed). All digits, whether doubled or not, are then added together. If the total is a multiple of 10 (total mod 10 equals 0), the number is considered valid under the algorithm. To compute a check digit for a base number, you perform the same doubling on the base digits (excluding the check digit) to obtain a sum, and choose the check digit so that the final total is a multiple of 10. Concretely, check digit = (10 - (sum mod 10)) mod 10.

Example: the base sequence 7992739871 yields a check digit of 3, producing the full number 79927398713, which passes the Luhn check.

Origin and usage: the algorithm was devised by Hans Peter Luhn in the 1950s while working for IBM. It has since become a standard, particularly for validating card numbers issued by payment networks, as well as various identification schemes and industry standards.

Limitations: the modulo 10 method is a simple checksum and is not designed for cryptographic security. It can detect many single-digit errors and adjacent transpositions but is not foolproof against deliberate tampering or certain error patterns.