# The Luhn Algorithm

Created by the german IBM scientist Hans Peter Luhn, the Luhn Algorithm is a checksum formula being used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers etc.

In this blog post, I will show you some functions I created that uses this algorithm. It can be used to calculate a checksum digit from a number, as well as validate numbers using the Luhn Algorithm checksum validation.

First off we have the main function, Get-LuhnChecksum. This function takes a number (uint64) as input and calculates the Luch checksum. This checksum is then used by either New-LuhnChecksumDigit to get the checksum digit of a number, or by Test-IsLuhnValid to validate a number, such as a credit card number.

Let’s demonstrate. We start off with a random number; 387234876. Let’s calculate the Luhn checksum digit for this number: As you see, the result is 2. This is our checksum digit. We append this number to the end of our original number, so we now have 3872348762. We can further validate this number: There you go. We have created a number with a Luhn checksum digit (last digit), and we have the means to validate it to see that it correct.

As stated earlier, this algorithm can be used to validate credit card numbers. It will detect any single digit error as well as almost all transpositions of adjacent digits. But since it’s not perfect, if you need credit card number validations you should add additional checks (such as number length).

Enjoy. If you have any questions, suggestions or bug-reports, please let me know in the comments section below (or on Twitter).

 function Get-LuhnChecksum { <# .SYNOPSIS Calculate the Luhn checksum of a number. .DESCRIPTION The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the US, and Canadian Social Insurance Numbers. It was created by IBM scientist Hans Peter Luhn. .EXAMPLE Get-LuhnChecksum -Number 1234567890123452 Calculate the Luch checksum of the number. The result should be 60. .INPUTS System.UInt64 .NOTES Author: Øyvind Kallstad Date: 19.02.2016 Version: 1.0 Dependencies: ConvertTo-Digits .LINKS #> [CmdletBinding()] param ( [Parameter(Mandatory = \$true, Position = 0, ValueFromPipeline = \$true)] [ValidateNotNullOrEmpty()] [uint64] \$Number ) \$digitsArray = ConvertTo-Digits –Number \$Number [array]::Reverse(\$digitsArray) \$sum = 0 \$index = 0 foreach (\$digit in \$digitsArray) { if ((\$index % 2) -eq 0) { \$doubledDigit = \$digit * 2 if (-not(\$doubledDigit -eq 0)) { \$doubleDigitArray = ConvertTo-Digits –Number \$doubledDigit \$sum += (\$doubleDigitArray | Measure-Object –Sum | Select-Object –ExpandProperty Sum) } } else { \$sum += \$digit } \$index++ } Write-Output \$sum } function New-LuhnChecksumDigit { <# .SYNOPSIS Calculate the Luhn checksum digit for a number. .DESCRIPTION This function uses the Luhn algorithm to calculate the Luhn checksum digit for a (partial) number. .EXAMPLE New-LuhnChecksumDigit -PartialNumber 123456789012345 This will get the checksum digit for the number. The result should be 2. .INPUTS System.UInt64 .NOTES Author: Øyvind Kallstad Date: 19.02.2016 Version: 1.0 Dependencies: Get-LuhnCheckSum .LINKS #> [CmdletBinding()] param ( [Parameter(Mandatory = \$true, Position = 0, ValueFromPipeline = \$true)] [uint64] \$PartialNumber ) \$checksum = Get-LuhnCheckSum –Number \$PartialNumber Write-Output ((\$checksum * 9) % 10) } function Test-IsLuhnValid { <# .SYNOPSIS Valdidate a number based on the Luhn Algorithm. .DESCRIPTION This function uses the Luhn algorithm to validate a number that includes the Luhn checksum digit. .EXAMPLE Test-IsLuhnValid -Number 1234567890123452 This will validate whether the number is valid according to the Luhn Algorithm. .INPUTS System.UInt64 .OUTPUTS System.Boolean .NOTES Author: Øyvind Kallstad Date: 19.02.2016 Version: 1.0 Dependencies: Get-LuhnCheckSum, ConvertTo-Digits .LINKS #> [CmdletBinding()] param ( [Parameter(Mandatory = \$true, Position = 0, ValueFromPipeline = \$true)] [uint64] \$Number ) \$numberDigits = ConvertTo-Digits –Number \$Number \$checksumDigit = \$numberDigits[-1] \$numberWithoutChecksumDigit = \$numberDigits[0..(\$numberDigits.Count – 2)] -join '' \$checksum = Get-LuhnCheckSum –Number \$numberWithoutChecksumDigit if (((\$checksum + \$checksumDigit) % 10) -eq 0) { Write-Output \$true } else { Write-Output \$false } }

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LuhnAlgorithm.ps1
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Oh.. and  you need this helper-function as well:

 function ConvertTo-Digits { <# .SYNOPSIS Convert an integer into an array of bytes of its individual digits. .DESCRIPTION Convert an integer into an array of bytes of its individual digits. .EXAMPLE ConvertTo-Digits 145 .INPUTS System.UInt64 .LINK .NOTES Author: Øyvind Kallstad Date: 09.05.2015 Version: 1.0 #> [OutputType([System.Byte[]])] [CmdletBinding()] param( [Parameter(Position = 0, Mandatory = \$true, ValueFromPipeline = \$true)] [uint64]\$Number ) \$n = \$Number \$numberOfDigits = 1 + [convert]::ToUInt64([math]::Floor(([math]::Log10(\$n)))) \$digits = New-Object Byte[] \$numberOfDigits for (\$i = (\$numberOfDigits – 1); \$i -ge 0; \$i—) { \$digit = \$n % 10 \$digits[\$i] = \$digit \$n = [math]::Floor(\$n / 10) } Write-Output \$digits }

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ConvertTo-Digits.ps1
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