EP4: Luhn's Algorithm: The algorithm behind checking your card on shopping sites

Ever wondered how websites like Amazon, Uber, or any other payment platforms ensure that your credit or debit card details are valid even before charging you? The secret lies in a fascinating tool known as Luhn’s Algorithm!

Luhn’s Algorithm is a simple yet effective mathematical method used to validate credit and debit card numbers. Invented by Hans Peter Luhn, a computer scientist at IBM in the 1950s, it has become the cornerstone for card number verification worldwide.

When you enter your card number during a transaction, the backend system performs a quick and invisible check using this algorithm. Here’s a brief look at the steps:

1. Reverse the Card Number: Start by reversing the digits of the card number.

2. Double Every Second Digit: From the reversed number, double every second digit. If the result is two digits (like 12), sum the two digits (1 + 2 = 3).

3. Sum It Up: Add all the resulting numbers together, including the digits that weren’t doubled.

4. Check Modulus 10: If the total sum is divisible by 10 (i.e., the remainder is 0), the card number is valid. Otherwise, it’s invalid.

function isValid(cardNumber[1..length])
    sum := 0
    parity := length mod 2
    for i from 1 to length do
        if i mod 2 != parity then
            sum := sum + cardNumber[i]
        elseif cardNumber[i] > 4 then
            sum := sum + 2 * cardNumber[i] - 9
        else
            sum := sum + 2 * cardNumber[i]
        end if
    end for
    return cardNumber[length] == ((10 - (sum mod 10)) mod 10)
end function

Let’s validate the card number 4532 1234 5678 9010:

1. Reverse: 0109 8765 4321 2354

2. Double every second digit: 0, 2, 0, 18, 8, 12, 4, 10, 4, 6, 2, 4, 2, 6, 4, 10
   (Sum the digits of two-digit numbers: 1 + 8 = 9, 1 + 2 = 3, etc.)

3. Add all the digits: 0 + 2 + 0 + 9 + 8 + 3 + 4 + 1 + 4 + 6 + 2 + 4 + 2 + 6 + 4 + 1 = 56

4. Modulus 10: 56 % 10 = 6 (Not valid!)

• Efficiency: It provides a quick way to weed out obvious errors, like typos in card numbers.

• Security: It prevents fraudulent or accidental submission of invalid numbers.

• Universal Application: Luhn’s Algorithm is used not just for credit cards but also for validating various other identification numbers like IMEI codes for phones.

So, the next time you buy something online or hail a ride, know that Luhn’s Algorithm is working silently in the background, ensuring the authenticity of your card details.

Want to learn more about the tech powering our everyday lives? Stay tuned for our next issue!