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
	https://en.wikipedia.org/wiki/Luhn_algorithm
	https://communary.wordpress.com/
	https://github.com/gravejester/Communary.ToolBox
	#>
	[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
	https://en.wikipedia.org/wiki/Luhn_algorithm
	https://communary.wordpress.com/
	https://github.com/gravejester/Communary.ToolBox
	#>
	[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
	https://en.wikipedia.org/wiki/Luhn_algorithm
	https://communary.wordpress.com/
	https://github.com/gravejester/Communary.ToolBox
	#>
	[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
	}
	}

view raw

LuhnAlgorithm.ps1

hosted with ❤ by GitHub

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
	https://communary.wordpress.com/
	https://github.com/gravejester/Communary.ToolBox
	.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
	}