LUHN Algorithm Logic

Algorithm for the Luhn Formula

LUHN Algorithm in C# (Validate Credit Card)

Credit Card validation LUHN algorithm using C

LUHN Algorithm – Validate credit card – in PHP

Validate the credit card (plsql code)!

Here’s how the algorithm for the Luhn formula works. Starting with a given credit card number,

1 2 3 4 – 5 6 7 8 – 9 0 1 2 – 3 4 5 2

we reverse the number, removing any non-numeric characters, to create a new string of digits like this (note that the checksum is now the first digit):

2 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1

Now we’ll look at each individual digit. Starting with the second digit in the string, we double every other number. The others are left alone.

2 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1

This creates a new string of digits shown here:

2 10 4 6 2 2 0 18 8 14 6 10 4 6 2 2

Finally, we go through this new string and add up each single digit to produce a total. In other words, for this example, we don’t add 2 + 10 + … but 2 + 1 + 0 + … instead:

2 + 1 + 0 + 4 + 6 + 2 + 2 + 0 + 1 + 8 + 8 + 1 + 4 + 6 + 1 + 0 + 4 + 6 + 2 + 2 = 60

Use your browser’s

option to see the full source code.

If this sum is an integer multiple of 10 (e.g., 10, 20, 30, 40, 50,…) then the card number is valid, as far as the checksum is concerned.

Here is the JavaScript code to sum the digits, where

represents the card number as a string of digits already in reverse order.

  // Run through each single digit to create a new string. Even digits
  // are multiplied by two, odd digits are left alone.

  t = "";
  for (i = 0; i < r.length; i++) {
    c = parseInt(r.charAt(i), 10);
    if (i % 2 != 0)
      c *= 2;
    t = t + c;
  }

  // Finally, add up all the single digits in this string.

  n = 0;
  for (i = 0; i < t.length; i++) {
    c = parseInt(t.charAt(i), 10);
    n = n + c;
  }

Once the sum is found, the code checks to see if it’s an even multiple of ten (i.e., n % 10 leaves no remainder).

  // If the resulting sum is an even multiple of ten (but not zero), the
  // card number is good.

  if (n != 0 && n % 10 == 0)
    return true;
  else
    return false;
}

Programming Note

You may have noticed that the checksum digit (2) is included in the sum. Rather than adding up the other digits and calculating the valid checksum value for comparison, it’s included in the total to save some programming steps.

In other words, if you were creating a new card number and wanted to find the right checksum digit, you’d total up the other digits as shown above except that you wouldn’t have the initial digit (2).

1 + 0 + 4 + 6 + 2 + 2 + 0 + 1 + 8 + 8 + 1 + 4 + 6 + 1 + 0 + 4 + 6 + 2 + 2 = 58

Using the total (58) you’d take the next highest number that is evenly divisible by ten and subtract the total from this to produce the proper checksum digit (60 – 58 = 2 in this case).

If the total was already an even multiple of ten, say 70, the checksum would simply be zero.

To save a couple of steps in the code, the checksum digit is included in the calculation so that the sum should be an integer multiple of ten.