Verhoeff

The Verhoeff algorithm is a checksum formula used to detect transcription errors in identification numbers. It is more powerful than the simpler Luhn algorithm, and catches all single-digit errors, as well as all transposition errors of adjacent digits. The algorithm was devised by Dutch mathematician Jacobus Verhoeff, and published in 1969.

The Verhoeff algorithm operates on a string of digits and produces a single check digit. This check digit is then appended to the original string. To validate a string that has a Verhoeff check digit, the algorithm is run on the entire string, including the check digit. If the result is zero, the string is considered valid.

The algorithm employs a multiplication table, a permutation table, and an inversion table for its calculation. These tables define how the digits are combined at each step.

Compared to other checksum algorithms like Luhn, Verhoeff is more robust in detecting a wider range of errors. However, its complexity makes it less commonly used in situations where a simple checksum is sufficient. Its strength lies in its ability to catch common data entry errors, particularly in scenarios requiring high accuracy and reliability.