C++: Using the Luhn Algorithm to Validate the CheckSum in the Personnummer Supplied in User Input

The Swedish Personnummer uses a variant of the Luhn Algorithm to generate a checksum (technically, a check digit) value that is is appended to the end of the personnummer. So, forexample, the nine-digit number YYMMDD-SSS would become YYMMDD-SSSC with the tenth digit being the checksum.

The model for generating the checksum is created by multiplying the alternating digits by a 2 or a 1 and, then, adding the sum of the products. In the nine-digit series, this means 212121212. So, for example, the number 010214-010 would become (0x2) + (1×1) + (0x2) + (2×1) + (1×2) + (4×1) + (0x2) + (1×1) + (0x2). When the product is greater than nine, the sum of those numbers is added. So, for example, 2×7 = 14 –> 1 + 4 = 5 and, thus, our result would be five for that single instance of digit.

The last number in the sum is then subtracted from 10 to create the checksum number. So, for example, 46 –> 6 and 10-6 = 4, and 4 becomes our checksum value.

Below is an C++ program to validate the checksum for the provided personnumer, given in the user-input. PersonnummerSet is merely a struct of ints that I’ve created in a header file, so that it can be referenced by other libraries (either by direct assignment to type or pointer). StringMagic is another header file that uses std::string.erase/std::remove to remove the ‘-‘ character from the input (Swedish Personnummers are always written as YYMMDD-SSSC.)

#include <cstring> // Replacing the old and busted with the new hotness.
#include <iomanip>
#include <iostream>
#include <cstdio> // Replacing the old and busted with the new hotness.
#include "Personnummerset.h"
#include "StringMagic.h"

class Personnummer
{
public:
    /**
     *  The PersonNumber is a property of type PersonnnummerSet, which is used to process the digits
     *  from the personnummer provided.
     */
    PersonnummerSet PersonNumber {};

    /**
     *  Initializes a new instance of the <see cref="Personnummer" /> class.
     * @param number - The converted long from the user's input.
     */
    explicit Personnummer(long number)
    {
        // We separate the three digit serial to future-proof for deriving sex of the individual in future checks.
        this->PersonNumber.Year = static_cast<int>(number / 100000000 % 100);   // First 2 integers     (0&1)
        this->PersonNumber.Month = static_cast<int>(number / 1000000 % 100);    // Second 2 integers    (2&3)
        this->PersonNumber.Day = static_cast<int>(number / 10000 % 100);        // Third 2 integers     (4&5)
        this->PersonNumber.SerialNumber = static_cast<int>(number / 100 % 100); // Fourth 2 integers    (6&7)
        this->PersonNumber.Sex = static_cast<int>(number / 10 % 10);            // First 1 integer      (8)
        this->PersonNumber.CheckSum = static_cast<int>(number % 10);            // Second 1 integer     (9)
    }

public:
    /**
     *  Generates the Luhn Algorithm checksum and compares that from the checksum given from the user's input.
     * @return A boolean indicating of the calculated checksum matches the provided checksum.
     */
    bool ValidateCheckSum()
    {
        return this->PersonNumber.CheckSum == this->GenerateChecksum();
    }

private:
    /**
     * This is a variation of the Luhn Algorithm, which is used to generate the checksum from the
     * first nine digits of the personnummer. Each value in the first nine digits is multiplied by
     * either a 2 or a 1. See: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2773709/figure/Fig1/
    */
    int GenerateChecksum()
    {
        int firstCheck;
        int fifthCheck;
        int seventhCheck;
        int ninthCheck;
        int firstYear = PersonNumber.Year > 9 ? PersonNumber.Year / 10 % 10 : 0;
        int secondYear = PersonNumber.Year%10;
        int firstMonth = PersonNumber.Month > 9 ? PersonNumber.Month / 10 % 10 : 0;
        int secondMonth = PersonNumber.Month%10;
        int firstDay = PersonNumber.Day > 9 ? PersonNumber.Day / 10 % 10 : 0;
        int secondDay = PersonNumber.Day%10;
        int firstSerial = PersonNumber.SerialNumber/10%10;
        int secondSerial = PersonNumber.SerialNumber%10;

        int firstYearDigit = firstYear * 2;
        if (firstYearDigit > 9)
        {
            int firstSum = firstYearDigit/10%10;
            int secondSum = firstYearDigit%10;
            firstCheck = firstSum + secondSum;
        }
        else
        {
            firstCheck = firstYearDigit;
        }

        int secondCheck = secondYear * 1;
        int thirdCheck = firstMonth * 2;
        int fourthCheck = secondMonth * 1;
        int firstDayCheck = firstDay * 2;
        if(firstDayCheck > 9)
        {
            int firstSum = firstDayCheck/10%10;
            int secondSum = firstDayCheck%10;
            fifthCheck = firstSum + secondSum;
        }
        else
        {
            fifthCheck = firstDayCheck;
        }

        int sixthCheck = secondDay * 1;
        int firstDigitRandom = firstSerial * 2;
        if (firstDigitRandom > 9)
        {
            int firstSum = firstDigitRandom/10%10;
            int secondSum = firstDigitRandom%10;
            seventhCheck = firstSum + secondSum;
        }
        else
        {
            seventhCheck = firstDigitRandom;
        }

        int eighthCheck = secondSerial * 1;
        int sexCheck = PersonNumber.Sex * 2;
        if(sexCheck > 9)
        {
            int firstSum = sexCheck/10%10;
            int secondSum = sexCheck%10;
            ninthCheck = firstSum + secondSum;
        }
        else
        {
            ninthCheck = sexCheck;
        }

        int sum = firstCheck + secondCheck + thirdCheck + fourthCheck + fifthCheck + sixthCheck + seventhCheck + eighthCheck + ninthCheck;
        int lastOfSum = sum%10;
        int checkSum = 10 - lastOfSum;
        return checkSum;

    }
};

int main()
{
    std::string user_input;
    std::cout << "Enter Personnummer (YYMMDD-SSSC): " << std::endl;
    std::cin >> user_input;

    // Necessary or the long conversion treats '-' or '+' as a delimiter.
    // NOTE: People aged over 99 will always have '+' in their personnummer.
    if(user_input.find('-') != std::string::npos)
    {
        StringMagic::RemoveDashFromString(user_input);
    }
    else if (user_input.find('+') != std::string::npos)
    {
        StringMagic::RemovePlusFromString(user_input);
    }

    // Smart-pointers are the future...
    std::unique_ptr<Personnummer> personNumber (new Personnummer(std::stol(user_input)));
    std::cout << std::boolalpha;
    std::cout << "CheckSum Passes: " << personNumber->ValidateCheckSum() << std::endl;

    personNumber.reset();
}

The above code can be used to validate almost any personnummer – save for those individuals whom are over 99 years of age, as the separator changes from ‘-‘ to ‘+’.

…and that’s about the extent of fun with Swedish Personnummers in C++ that this post will cover.

Thanks for coming to this NERDTalk™ and happy programming!