In the world of electronic payments and online transactions where security is paramount, credit card validation algorithms play an important role. One of the most widely used algorithms, which helps not only to prevent errors when entering card numbers, but also to detect possible fraud attempts, is the Luhn algorithm, also known as the “Luhn algorithm”.
The Luhn algorithm was developed by mathematician Hans Peter Lun in 1954 and has since become the standard method for checking the validity of credit card numbers in many payment systems. It is based on a simple mathematical operation and a checksum, which is calculated from the digits of the card number.

In this article, I will describe how the Luhn algorithm works, its main steps and application. We will also discuss its weaknesses and uses, as well as take a look at PHP and Python code examples to help you understand how you can implement this algorithm in your projects.

Understanding the Luhn algorithm is important not only for developers and financial technology professionals, but also for users who want to be aware of the security of their payments and transactions. Let’s get started and understand this key credit card number verification algorithm.

Luhn’s algorithm is based on a simple principle. It verifies a credit card number based on its checksum. The checksum is a number that is calculated from certain digits in the card number and is used to check its correctness.

Here are the basic steps of Luhn’s algorithm:
1. Isolate the last digit in the credit card number. This will be the check digit.
2. Turn over the remaining digits in the card number.
3. Double the value of every second digit, starting with the first digit after the check digit (that is, the second, fourth, sixth, etc.), and reduce the result to one digit by adding the digits of the number if it is greater than 9.
4. Add all the digits of the resulting number together.
5. Add the check digit (step 1) to the sum (step 4).
6. If the total is divisible by 10 without a remainder, then the credit card number is valid. Otherwise, it is considered invalid.

The Luhn algorithm is used by many payment processing systems to validate credit card numbers before processing them. It helps to identify typos, input errors or invalid card numbers, thus improving the accuracy and security of payment systems.

It is important to note that the Luhn algorithm does not check the existence of a real account or the validity of the card, but only checks the correctness of the card number itself. Checking the validity of the card requires communication with payment gateways or banking systems.

Luhn’s algorithm can be used not only to validate credit card numbers, but also to validate other identification numbers and digit sequences. Here are some examples where this algorithm can be applied:
1. Validation of bank account numbers: Some banking systems may use the Luhn algorithm to validate bank account numbers and ensure that data is entered correctly when making payments or transfers.
2. Checking social security numbers: Various countries use social security identification numbers or national identification cards. Luhn’s algorithm can be used to check the validity of these numbers and prevent erroneous input.
3. Validation of passport numbers: Luhn’s algorithm can be used to check passport numbers and confirm their correctness during check-in, ticket booking and other processes related to passenger identification.
4. Barcode Validation: Some types of barcodes such as EAN (European Article Number) or UPC (Universal Product Code) can also be checked with the Luhn algorithm to detect possible errors or incorrect format.
5. Validation of other identification numbers: The Luhn algorithm can be used to validate various identification numbers, such as driver’s license numbers, insurance policy numbers, and other forms of identification where verification of numerical sequences is required.

In general, Luhn’s algorithm can be used in any situation where it is necessary to check the correctness of numerical identification numbers or digit sequences.

Generating valid credit card numbers that match the Luhn algorithm is a difficult task because it involves not only generating the number correctly, but also compliance with certain rules used in credit card systems, so using the Luhn algorithm to generate credit card numbers will not work 😉

Because the Luhn algorithm is quite simple – it has some weak points:
1. Does not provide verification of the existence of a real account: the Luhn algorithm only checks the correctness of the credit card number, but does not confirm that the account or card associated with it exists or is valid. To check the validity of the card, you need to contact payment gateways or banking systems.
2. Does not detect all types of errors: Luhn’s algorithm may not detect some types of errors in credit card numbers. For example, it cannot detect random permutations of digits or substitutions of some digits for others if the checksum is preserved.
3. Limited by card number formats: The Luhn algorithm is designed to check credit card numbers that follow certain formats, such as Visa, Mastercard, American Express, etc. If the card number does not match these formats, the algorithm may give an incorrect result.
4. Does not take into account other aspects of security: the Luhn algorithm is not designed to check other aspects of credit card security, such as checking the CVV code, card expiration date, card holder identification, and other protective measures. It only checks the digital correctness of the card number.
5. Possibility of guessing numbers: since the Luhn algorithm is based on the calculation of the checksum, there is a small chance that attackers can guess the actual card number by trying all possible combinations. This can be a problem if no other fraud detection methods are used in the verification process.

Now let’s see a code example that allows you to implement the Luhn algorithm in PHP:

function luhnAlgorithm($number) {
$number = strrev(preg_replace('/[^0-9]/', '', $number)); // Flip the number and remove all non-digit characters
$sum = 0;
 
for ($i = 0, $length = strlen($number); $i < $length; $i++) {
$digit = intval($number[$i]);
 
if ($i % 2 === 1) {
$digit *= 2;
if ($digit > 9) {
$digit -= 9;
}
}
 
$sum += $digit;
}
 
return $sum % 10 === 0;
}
 
// Usage example
$cardNumber = '4532015112830366';
if (luhnAlgorithm($cardNumber)) {
echo 'Card number is valid.';
} else {
echo 'Card number is invalid.';
}

In this example, the luhnAlgorithm() function takes a credit card number as a string and returns true if the number is valid and false if the number is invalid, according to Luhn’s algorithm.

It is important to note that the implementation may vary depending on the specific requirements and context of use. This is just a basic example that you can modify and adapt to your needs.

And now – an example of the implementation of the Luhn algorithm in Python:

def luhn_algorithm(number):
number = str(number)[::-1].replace(" ", "")  # Flip the number and remove all spaces
sum = 0
for i in range(len(number)):
digit = int(number[i])
if i % 2 == 1:
digit *= 2
if digit > 9:
digit -= 9
sum += digit
return sum % 10 == 0
# Usage example
card_number = "4532 0151 1283 0366"
if luhn_algorithm(card_number):
print("Card number is valid.")
else:
print("Card number is invalid.")

In this example, the luhn_algorithm() function takes a credit card number as a string and returns True if the number is valid and False if the number is invalid, according to Luhn’s algorithm.

Please note that the implementation is subject to change and adaptation to specific requirements and context of use. The example is provided for basic understanding and may require additional processing to work with different credit card number formats.

Actually – that’s all I could say about the Luhn algorithm. As always – in case of questions – write to the mail or Telegram.