Luhn Algorithm

Luhn Algorithm

The Luhn algorithm (also called the Modulus 10 or MOD 10 algorithm) is a simple checksum formula used to validate identification numbers. It’s widely used in payment systems to check credit card numbers and in other contexts where quick detection of input errors is needed.

Key points

• Developed in the 1950s, the Luhn algorithm verifies that a number sequence has been entered correctly by computing a check value (a check digit).
• It is not a proof of authenticity or fraud prevention — it mostly detects accidental errors, such as mistyped digits.
• It’s easy to implement and is included in many programming libraries and payment-processing systems.

How the algorithm works (step-by-step)

To validate a number that already includes a check digit (the final digit):
1. Starting from the rightmost digit (the check digit), move left and double every second digit.
2. If doubling produces a value greater than 9, subtract 9 from it (equivalently, sum the digits of the product).
3. Sum all the resulting digits (the doubled ones after reduction and the untouched ones).
4. If the total modulo 10 is 0, the number is valid under Luhn; otherwise it’s invalid.

To compute a check digit for a number missing it:
1. Append a placeholder digit (usually 0) as the check digit.
2. Run the validation steps above to get the total.
3. The correct check digit is (10 − (total mod 10)) mod 10.

Example

Validate 79927398713:
* Digits (left to right): 7 9 9 2 7 3 9 8 7 1 3
* From the right, double every second digit and reduce >9 by subtracting 9:
* … 3, (1→2), 7, (8→7), 9, (3→6), 7, (2→4), 9, (9→9), 7
* Sum = 70 → 70 mod 10 = 0 → valid

Uses

• Credit card number validation during data entry and transaction processing
• Validating other identification numbers that embed a check digit (some national IDs, IMEI, etc.)
• Quick detection of accidental input errors in forms and systems

What is a MOD 10 error?

A MOD 10 error indicates that an identification number failed the Luhn (modulus 10) checksum test — i.e., the computed checksum doesn’t match, usually meaning a digit was mistyped.

Limitations

• Luhn detects all single-digit errors and many adjacent transposition errors, but not all possible mistakes. Some swaps of adjacent digits can produce the same checksum and go undetected.
• It does not authenticate a card or guarantee the issuer is legitimate. It only helps catch accidental typos.

Implementation notes

• The algorithm is compact and efficient; it’s commonly implemented in many languages and available in libraries for rapid integration.
• For production systems, combine Luhn checks with other validation layers (format checks, issuer identification, authorization checks) to reduce fraud and errors.

Bottom line

The Luhn algorithm is a simple, effective checksum used across payment systems to catch common data-entry errors in identification numbers. It’s fast and easy to implement but should be seen as an error-detection tool rather than a security or authenticity measure.