Luhn mod N algorithm - Revision history

MrOllie: Restored revision 1287924155 by Tc14Hd (talk)

2025-05-06T14:17:01Z

Restored revision 1287924155 by Tc14Hd (talk)

← Previous revision		Revision as of 14:17, 6 May 2025
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	{{unreferenced\|date=May 2010}}		{{unreferenced\|date=May 2010}}
	{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}		{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}
	The '''Luhn mod ''N'' algorithm''' is an extension to the [[Luhn algorithm]] (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered [[Radix\|base]]. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of {{Var\|N}} characters where {{Var\|N}} is divisible by 2.<ref>GeeksforGeeks. (2024). Generation of Programming Languages. Retrieved May 2, 2025, from [https://www.geeksforgeeks.org/generation-programming-languages/](https://www.geeksforgeeks.org/generation-programming-languages/)</ref>		The '''Luhn mod ''N'' algorithm''' is an extension to the [[Luhn algorithm]] (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered [[Radix\|base]]. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of {{Var\|N}} characters where {{Var\|N}} is divisible by 2.

	== Informal explanation ==		== Informal explanation ==
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	* [[International Securities Identification Number]] (ISIN)		* [[International Securities Identification Number]] (ISIN)

	== References ==
	GeeksforGeeks. (2024). Generation of Programming Languages. Retrieved May 2, 2025, from [https://www.geeksforgeeks.org/generation-programming-languages/](https://www.geeksforgeeks.org/generation-programming-languages/)

	Evanion. (n.d.). luhn: A Luhn mod-N Library. Retrieved May 2, 2025, from [https://github.com/Evanion/luhn](https://github.com/Evanion/luhn)
	[[Category:Modular arithmetic]]		[[Category:Modular arithmetic]]
	[[Category:Checksum algorithms]]		[[Category:Checksum algorithms]]

MrRestre11: references

2025-05-05T15:17:38Z

references

← Previous revision		Revision as of 15:17, 5 May 2025
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	{{unreferenced\|date=May 2010}}		{{unreferenced\|date=May 2010}}
	{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}		{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}
	The '''Luhn mod ''N'' algorithm''' is an extension to the [[Luhn algorithm]] (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered [[Radix\|base]]. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of {{Var\|N}} characters where {{Var\|N}} is divisible by 2.		The '''Luhn mod ''N'' algorithm''' is an extension to the [[Luhn algorithm]] (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered [[Radix\|base]]. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of {{Var\|N}} characters where {{Var\|N}} is divisible by 2.<ref>GeeksforGeeks. (2024). Generation of Programming Languages. Retrieved May 2, 2025, from [https://www.geeksforgeeks.org/generation-programming-languages/](https://www.geeksforgeeks.org/generation-programming-languages/)</ref>

	== Informal explanation ==		== Informal explanation ==
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	* [[International Securities Identification Number]] (ISIN)		* [[International Securities Identification Number]] (ISIN)

			== References ==
			GeeksforGeeks. (2024). Generation of Programming Languages. Retrieved May 2, 2025, from [https://www.geeksforgeeks.org/generation-programming-languages/](https://www.geeksforgeeks.org/generation-programming-languages/)

			Evanion. (n.d.). luhn: A Luhn mod-N Library. Retrieved May 2, 2025, from [https://github.com/Evanion/luhn](https://github.com/Evanion/luhn)
	[[Category:Modular arithmetic]]		[[Category:Modular arithmetic]]
	[[Category:Checksum algorithms]]		[[Category:Checksum algorithms]]

Tc14Hd: Updated short description

2025-04-29T08:27:52Z

Updated short description

← Previous revision		Revision as of 08:27, 29 April 2025
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	{{Short description\|Extension of the Luhn algorithm ~~to arbitrary bases~~}}		{{Short description\|Extension of the Luhn algorithm}}
	{{unreferenced\|date=May 2010}}		{{unreferenced\|date=May 2010}}
	{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}		{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}

Tc14Hd: Added short description

2025-04-29T08:27:02Z

Added short description

← Previous revision		Revision as of 08:27, 29 April 2025
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			{{Short description\|Extension of the Luhn algorithm to arbitrary bases}}
	{{unreferenced\|date=May 2010}}		{{unreferenced\|date=May 2010}}
	{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}		{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}

Tc14Hd: /* Limitation */ Changed capitalization again

2025-04-29T08:26:07Z

Limitation: Changed capitalization again

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	== Limitation ==		== Limitation ==

	The Luhn mod N algorithm only works where {{var\|N}} is divisible by 2. This is because there is an operation to correct the value of a position after doubling its value which does not work where {{var\|N}} is not divisible by 2. For applications using the [[English alphabet]] this is not a problem, since a string of lower-case letters has 26 code-points, and adding [[~~Decimal~~]] characters adds a further 10, maintaining an {{var\|N}} divisible by 2.		The Luhn mod N algorithm only works where {{var\|N}} is divisible by 2. This is because there is an operation to correct the value of a position after doubling its value which does not work where {{var\|N}} is not divisible by 2. For applications using the [[English alphabet]] this is not a problem, since a string of lower-case letters has 26 code-points, and adding [[decimal]] characters adds a further 10, maintaining an {{var\|N}} divisible by 2.

	=== Explanation ===		=== Explanation ===

Tc14Hd: /* Limitation */ Changed capitalization

2025-04-29T08:24:56Z

Limitation: Changed capitalization

← Previous revision		Revision as of 08:24, 29 April 2025
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	=== Explanation ===		=== Explanation ===

	The second step in the [[Luhn algorithm]] re-packs the doubled value of a position into the original digit's [[Radix\|base]] by adding together the individual digits in the doubled value when written in [[Radix\|base]] {{var\|N}}. This step results in even numbers if the doubled value is less than or equal to {{var\|N}}, and odd numbers if the doubled value is greater than {{var\|N}}. For example, in [[~~Decimal~~]] applications where {{var\|N}} is 10, original values between 0 and 4 result in even numbers and original values between 5 and 9 result in odd numbers, effectively re-packing the doubled values between 0 and 18 into a single distinct result between 0 and 9.		The second step in the [[Luhn algorithm]] re-packs the doubled value of a position into the original digit's [[Radix\|base]] by adding together the individual digits in the doubled value when written in [[Radix\|base]] {{var\|N}}. This step results in even numbers if the doubled value is less than or equal to {{var\|N}}, and odd numbers if the doubled value is greater than {{var\|N}}. For example, in [[decimal]] applications where {{var\|N}} is 10, original values between 0 and 4 result in even numbers and original values between 5 and 9 result in odd numbers, effectively re-packing the doubled values between 0 and 18 into a single distinct result between 0 and 9.

	Where an {{var\|N}} is used that is not divisible by 2 this step returns even numbers for doubled values greater than {{var\|N}} which cannot be distinguished from doubled values less than or equal to {{var\|N}}.		Where an {{var\|N}} is used that is not divisible by 2 this step returns even numbers for doubled values greater than {{var\|N}} which cannot be distinguished from doubled values less than or equal to {{var\|N}}.

2.51.57.129: /* Algorithm in JavaScript */

2025-03-31T17:48:05Z

Algorithm in JavaScript

← Previous revision		Revision as of 17:48, 31 March 2025
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	</syntaxhighlight>		</syntaxhighlight>

	== ~~[[Algorithmic PC\|~~Algorithm]] in JavaScript ==		== Algorithm in JavaScript ==

	Assuming the following functions are defined:		Assuming the following functions are defined:

74.37.83.56: Agee downloa

2025-01-14T01:49:38Z

Agee downloa

← Previous revision		Revision as of 01:49, 14 January 2025
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	</syntaxhighlight>		</syntaxhighlight>

	== Algorithm in JavaScript ==		== [[Algorithmic PC\|Algorithm]] in JavaScript ==

	Assuming the following functions are defined:		Assuming the following functions are defined:

Frap: Italic n

2024-10-25T08:22:44Z

Italic n

← Previous revision		Revision as of 08:22, 25 October 2024
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	{{unreferenced\|date=May 2010}}		{{unreferenced\|date=May 2010}}
			{{DISPLAYTITLE:Luhn mod ''N'' algorithm}}
	The '''Luhn mod ''N'' algorithm''' is an extension to the [[Luhn algorithm]] (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered [[Radix\|base]]. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of {{Var\|N}} characters where {{Var\|N}} is divisible by 2.		The '''Luhn mod ''N'' algorithm''' is an extension to the [[Luhn algorithm]] (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered [[Radix\|base]]. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of {{Var\|N}} characters where {{Var\|N}} is divisible by 2.

24.126.63.128: /* Algorithm in C# */

2023-11-15T23:38:08Z

Algorithm in C#

← Previous revision		Revision as of 23:38, 15 November 2023
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	<syntaxhighlight lang="csharp">		<syntaxhighlight lang="csharp">
			/// <summary>
⚫	int CodePointFromCharacter(char character) {...}
			/// This can be any string of characters.
			/// </summary>
			private const string CodePoints = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";

		⚫	private int NumberOfValidInputCharacters() => CodePoints.Length;
⚫	char CharacterFromCodePoint(int codePoint) ~~{...}~~

		⚫	private int CodePointFromCharacter(char character) => CodePoints.IndexOf(character);
⚫	int NumberOfValidInputCharacters() ~~{..~~.}

		⚫	private char CharacterFromCodePoint(int codePoint) => CodePoints[codePoint];
	</syntaxhighlight>		</syntaxhighlight>