Strengths and Weaknesses
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 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.
Prepending a 0 to odd-length numbers enables you to process the number from left to right rather than right to left, doubling the odd-place digits.
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.
Read more about this topic: Luhn Algorithm
Famous quotes containing the words strengths and/or weaknesses:
“A man who has never lost himself in a cause bigger than himself has missed one of life’s mountaintop experiences. Only in losing himself does he find himself. Only then does he discover all the latent strengths he never knew he had and which otherwise would have remained dormant.”
—Richard M. Nixon (1913–1995)
“Much can be inferred about a man from his mistress: in her one beholds his weaknesses and his dreams.”
—G.C. (Georg Christoph)