Luhn Algorithm

The Luhn algorithm is a checksum algorithm used to detect errors in identification numbers, such as credit card numbers and IMEI numbers. It is a modulo-10 algorithm, which means that the sum of the digits in the number is divided by 10, and the remainder is used to determine whether the number is valid.

Algorithm:

1. Double every other digit: Starting from the rightmost digit, double every other digit in the number.
2. Sum the digits: Add all the digits in the number, including the doubled digits.
3. Modulo 10: Divide the sum by 10 and take the remainder.
4. Check for equality: If the remainder is 0, the number is valid. Otherwise, it is not.

Example:

Given the credit card number 1234 5678 9012:

1. Double every other digit: 1234 5678 9012 becomes 1234 1168 9012.
2. Sum the digits: 1234 1168 9012 = 3644.
3. Modulo 10: 3644 % 10 = 4.
4. Check for equality: Since the remainder is not 0, the number is not valid.

Variations:

• Luhn-2 algorithm: This algorithm doubles every other digit, but instead of adding the doubled digits, they are added as separate numbers.
• Luhn-3 algorithm: This algorithm doubles every third digit, and the sum of the doubled digits is divided by 10.

Applications:

The Luhn algorithm is used in a variety of applications, including:

• Credit card verification
• IMEI number validation
• Social Security number validation

Advantages:

• Simple to implement
• Effective at detecting errors
• Relatively secure

Disadvantages:

• Not foolproof: It is possible to create numbers that pass the Luhn algorithm but are not valid.
• Can be cracked with enough effort: With enough time and resources, it is possible to crack the Luhn algorithm.