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Did you know how Luhn checking bits reveal the secrets of digital errors?
In daily life, the correctness of identification numbers is critical, especially in financial transactions and government documents. In order to ensure the accuracy of these numbers, the Luhn algorithm came into being. This simple checksum formula can effectively verify the validity of multiple identification numbers and avoid disputes caused by typing errors.
The Luhn algorithm, or Modulo 10, is designed to protect numeric identification numbers from accidental errors and has been widely used in credit card and government identification numbers.
What is Luhn algorithm?
The Luhn algorithm was created by IBM scientist Hans Peter Luhn in 1960. Its purpose was to provide a simple way to verify whether some digital codes are valid. This algorithm is not cryptographically secure, but focuses on preventing accidental errors. According to the specifications of ISO/IEC 7812-1, the Luhn algorithm is widely used in many fields such as credit card numbers and social security numbers.
How to calculate the check bit?
The process of calculating check bits is quite simple:
- Remove existing check bits to get valid digits.
- From right to left, double every other digit. If the result is greater than 9, subtract 9.
- Add all numbers (including undoubled numbers).
- The calculation of the check bit can be understood as the following process: subtract the remainder of the sum (mod 10) from 10.
For example, for account number 1789372997, the calculated check digit is 4, and the complete account number is 17893729974.
Steps to verify check bits
To verify whether a number is valid, you first need to remove the check digit, and then recalculate the check digit according to the above steps. Finally, the calculated check bit is compared with the original check bit, and if they match, the number is valid.
Advantages and disadvantages of Luhn algorithm
The main advantage of Luhn's algorithm is that it effectively detects all single-digit errors and almost all swapping errors of adjacent digits. However, it cannot detect the conversion of 09 to 90, and when a Gemini error occurs, the check such as 22↔55 is also limited. Relatively more complex checksum algorithms such as Verhoeff's algorithm and Damm's algorithm can detect more transcription errors.
The special thing about Luhn's algorithm is that, for verification purposes, leading zeros in the numbers do not affect the final calculation result.
Many uses of Luhn algorithm
The application range of Luhn algorithm is almost ubiquitous, including but not limited to:
- Credit card number
- IMEI number
- US National Provider Identifier
- Canadian Social Security Number
- Israeli ID number
- South African identity card number
- Swedish national identity card number
- Greek Social Security Number
- ICCID of SIM card
- USPS Package Tracking Number
- Italian VAT number
Future Outlook
With the rapid development of digitalization, the application of Luhn algorithm will become more and more widespread. From electronic payments to identity verification, the security and accuracy of digital identification will be a top priority in the design of many systems. In the future, more innovative check code algorithms may appear to further improve security and reliability.
In the digital world, can we ensure that each set of numbers is accurate and effectively use checking algorithms to ensure the safety of our daily lives?
