What is the Luhn Algorithm?

The Luhn algorithm, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, and National Provider Identifier numbers in the US. It was developed by IBM scientist Hans Peter Luhn and patented in 1960.

The primary purpose of the Luhn algorithm is to protect against accidental errors, such as a mistyped digit. It is not a cryptographically secure hash function; it is designed to catch simple input errors, not to protect against malicious attacks.

How Does It Work?

The algorithm is applied to a number (or a string of digits) to verify its validity. Here’s a step-by-step breakdown of how it works:

1. Double Every Second Digit: Starting from the rightmost digit and moving left, double the value of every second digit.
2. Sum the Digits: If doubling a digit results in a two-digit number, add those two digits together to get a single-digit number (e.g., 14 becomes 1 + 4 = 5).
3. Sum All Digits: Add up all the digits in the resulting number (including the digits you didn't double).
4. Check the Modulo: If the total sum is divisible by 10 (i.e., the total modulo 10 is 0), then the number is valid according to the Luhn algorithm.

An Example

Let's validate the number 49927398716:

1. The Number: 4 9 9 2 7 3 9 8 7 1 6
2. Double every second digit from the right:
   • 1 becomes 2
   • 7 becomes 14
   • 9 becomes 18
   • 7 becomes 14
   • 9 becomes 18
3. The new numbers are: 4, (18), 9, (14), 7, (6), 9, (16), 7, (2), 6
4. Sum digits of doubled numbers:
   • 18 -> 1 + 8 = 9
   • 14 -> 1 + 4 = 5
   • 14 -> 1 + 4 = 5
   • 18 -> 1 + 8 = 9
5. The final digits to sum are: 4, 9, 9, 5, 7, 3, 9, 8, 7, 2, 6
6. Sum all digits: 4 + 9 + 9 + 5 + 7 + 3 + 9 + 8 + 7 + 2 + 6 = 70
7. Check Modulo 10: 70 % 10 = 0

Since the result is 0, the number 49927398716 is a valid number according to the Luhn check.

Why Is It Important for Developers?

For developers building e-commerce sites, payment forms, or any system that accepts credit card numbers, the Luhn algorithm is the first line of defense. By implementing a client-side or server-side Luhn check, you can:

• Reduce Errors: Instantly catch typos and data entry mistakes before the data is even sent to a payment processor.
• Improve User Experience: Provide immediate feedback to users if they've entered an invalid number, saving them from the frustration of a failed transaction later.
• Lower Processing Costs: Reduce the number of invalid requests sent to your payment gateway, which can sometimes incur fees.

Our own CCGen V2 tool uses this very algorithm to generate valid test numbers, and our Card Validator uses it to perform its initial check. It's a fundamental piece of the puzzle for financial data validation.