The Luhn formula is a simple checksum formula used for validating identification numbers. It is designed to protect against accidental errors in data entry but not malicious attacks. For example, on a website a user may enter a credit card number or ISBN and sometimes these numbers may be mistyped. One can then use the Luhn formula to determine if the entered number is a valid one.
The validation algorithm is as follows:
- From the rightmost digit, double the value of every other digit.
- If a doubled value has two digits then add the digits individually.
- The number is valid under the Luhn formula: if the sum of all the digits is divisible by 10
(sum mod 10 == 0)
For Example, consider the number 1762483. We want to determine if it is a valid identification number using the Luhn formula?
Number | 1 | 7 | 6 | 2 | 4 | 8 | 3 Double every other digit |1 | 14 | 6 | 4 | 4 | 16 | 3 Sum digit | 1 | 5 | 6 | 4 | 4 | 7 | 3
Total Sum = 1 + 5 + 6 + 4 + 4 + 7 + 3 = 30
The total sum (30) is divisible by 10 and hence 1762483 is valid under the Luhn formula.
Here is the actual implementation in python
def luhn_formula_validator(input):
'''Check the input number under the Luhn Formula
Parameters:
-----------
input: input number as sting.
Returns:
--------
boolean
'''
#convert digits to list
input_list = [int(x) for x in input]
position = 1
sum = 0
for number in input_list:
if position % 2 == 0:
number = number * 2
#sum individual digits of a doubled digit
if number > 9:
number = 1 + number % 10
sum += number
position += 1
return sum % 10 == 0