Comments on: Verhoeff’s Dihedral Group D5 Check http://en.dahnielson.com/2006/09/verhoeff.html Misleading the public since 1979 Sat, 22 Nov 2008 09:26:32 +0000 http://wordpress.org/?v=2.2.2 By: Anders Dahnielson http://en.dahnielson.com/2006/09/verhoeff.html#comment-2119 Anders Dahnielson Tue, 10 Apr 2007 09:57:52 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-2119 I believe this document <a href="http://labs.dahnielson.com/files/2006/09/19/adfa.pdf" rel="nofollow">"Numeric Department Identifiers"</a> by the Australian Defense Force Academy was my main reference when implementing the Verhoeff algorithm. I believe this document “Numeric Department Identifiers” by the Australian Defense Force Academy was my main reference when implementing the Verhoeff algorithm.

]]> By: Peter Harding http://en.dahnielson.com/2006/09/verhoeff.html#comment-2064 Peter Harding Wed, 04 Apr 2007 11:15:16 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-2064 It turns out that my client has made up lots of "units" using the numerical recipes version, so right or wrong they're going to go with that. I've retrieved Verhoeff's original paper but it's hard group theory maths -it looks the same upside down to me! I see the wikipedia article discussion cites yet another rendering of the scheme, also held to be incorrect. Without the input of a skilled mathematician (Verhoeff - are you reading us?) I guess nobody will ever really know! If you find your references I'd be interested to hear about them. Thanks for your input! It turns out that my client has made up lots of “units” using the numerical recipes version, so right or wrong they’re going to go with that. I’ve retrieved Verhoeff’s original paper but it’s hard group theory maths -it looks the same upside down to me! I see the wikipedia article discussion cites yet another rendering of the scheme, also held to be incorrect.

Without the input of a skilled mathematician (Verhoeff - are you reading us?) I guess nobody will ever really know! If you find your references I’d be interested to hear about them.

Thanks for your input!

]]> By: Anders Dahnielson http://en.dahnielson.com/2006/09/verhoeff.html#comment-2010 Anders Dahnielson Fri, 30 Mar 2007 14:44:30 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-2010 Here is a live version of my script to play around with: <code>http://labs.dahnielson.com/tmp/verhoeff-test.php?f=calc&n=142857</code> <ul><li><code>f</code> can either be <em>calc</em> or <em>check</em></li><li><code>n</code> is the number to calculate a check digit for or check</li></ul> If you calculate the check digit for <code>142857</code> it return <code>0</code> (and if you check <code>1428570</code> it return <code>0</code>). So my code looks like to be on the Wikipedia side of the table. Here is a live version of my script to play around with:

http://labs.dahnielson.com/tmp/verhoeff-test.php?f=calc&n=142857

  • f can either be calc or check
  • n is the number to calculate a check digit for or check

If you calculate the check digit for 142857 it return 0 (and if you check 1428570 it return 0). So my code looks like to be on the Wikipedia side of the table.

]]> By: Peter Harding http://en.dahnielson.com/2006/09/verhoeff.html#comment-2008 Peter Harding Fri, 30 Mar 2007 12:49:17 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-2008 I can't run PHP. If we take the example 142857, the wikipedia version gives 0 and the Numerical Recipes version gives 6. This site http://www.augustana.ab.ca/~mohrj/algorithms/checkdigit.html agrees with wikipedia, this one http://web.mit.edu/kenta/www/three/verhoeff-checksum.html.gz goes with Numerical Recipes. Num Rec has shot me in the foot before (giving code in a typeface where "one" and "ell" are identical!!), but it's generally held to be scholarly. I was going to try and surf some pictures of old german banknotes...! I can’t run PHP. If we take the example 142857, the wikipedia version gives 0 and the Numerical Recipes version gives 6. This site http://www.augustana.ab.ca/~mohrj/algorithms/checkdigit.html agrees with wikipedia, this one http://web.mit.edu/kenta/www/three/verhoeff-checksum.html.gz goes with Numerical Recipes. Num Rec has shot me in the foot before (giving code in a typeface where “one” and “ell” are identical!!), but it’s generally held to be scholarly. I was going to try and surf some pictures of old german banknotes…!

]]> By: Anders Dahnielson http://en.dahnielson.com/2006/09/verhoeff.html#comment-2006 Anders Dahnielson Fri, 30 Mar 2007 09:56:28 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-2006 I don't remember what text I used, don't think it was the Wikipedia article but some textbook or report on check digits. I probably have a couple PDF files with the text that I've downloaded somewhere, I will try to find them. Hmm... wonder what result my implementation match? Scary. I don’t remember what text I used, don’t think it was the Wikipedia article but some textbook or report on check digits. I probably have a couple PDF files with the text that I’ve downloaded somewhere, I will try to find them.

Hmm… wonder what result my implementation match? Scary.

]]> By: Peter Harding http://en.dahnielson.com/2006/09/verhoeff.html#comment-2005 Peter Harding Fri, 30 Mar 2007 09:42:30 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-2005 The results of the wikipedia article differ from the results of the recipe given in the "Numerical Recipes in C" book. I've found a website that agrees with the book (but maybe they used it!). I've retrieved Verhoeff's original paper but I'm not up on group theory - it looks the same upside down to me! Anyone know for sure that the wikipedia article is good? Are there any good other references around? Many thanks The results of the wikipedia article differ from the results of the recipe given in the “Numerical Recipes in C” book. I’ve found a website that agrees with the book (but maybe they used it!). I’ve retrieved Verhoeff’s original paper but I’m not up on group theory - it looks the same upside down to me!

Anyone know for sure that the wikipedia article is good? Are there any good other references around?

Many thanks

]]> By: Anders Dahnielson http://en.dahnielson.com/2006/09/verhoeff.html#comment-1831 Anders Dahnielson Wed, 07 Mar 2007 09:45:37 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-1831 The <code>calcsum($number)</code> function return the checksum digit for the series of digits used as argument, if you give it <code>142857</code> as argument it will return the checksum digit <code>0</code>. Append the digit to the number so it now reads <code>1428570</code>. The <code>checksum($number)</code> do the opposite. Give it a number with check digit to check, like <code>1428570</code>, as argument and will return a <code>0</code> if the number is valid (it will always be a zero if valid no matter what the check digit was). The Verhoeff algorithm have no limitation on the number of digits (as many other algorithms have) it can check, it's unlimited. The calcsum($number) function return the checksum digit for the series of digits used as argument, if you give it 142857 as argument it will return the checksum digit 0. Append the digit to the number so it now reads 1428570.

The checksum($number) do the opposite. Give it a number with check digit to check, like 1428570, as argument and will return a 0 if the number is valid (it will always be a zero if valid no matter what the check digit was).

The Verhoeff algorithm have no limitation on the number of digits (as many other algorithms have) it can check, it’s unlimited.

]]> By: mauricio http://en.dahnielson.com/2006/09/verhoeff.html#comment-1826 mauricio Wed, 07 Mar 2007 01:03:37 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-1826 thanks, still not clear what is the role of the calcsum() function. Also, what do you do when you have numbers with more than 8 digits total (like in a credit card)? thanks, still not clear what is the role of the calcsum() function. Also, what do you do when you have numbers with more than 8 digits total (like in a credit card)?

]]> By: Anders Dahnielson http://en.dahnielson.com/2006/09/verhoeff.html#comment-1780 Anders Dahnielson Wed, 28 Feb 2007 09:41:55 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-1780 For the benefit of all, I've realized that I could post my reply here as well: You asked about where the previous <em>c</em> value came from. I guess it is easier to follow the <a href="http://en.wikipedia.org/wiki/Verhoeff_algorithm#Example" rel="nofollow">example on Wikipedia</a> if you take a look at my PHP implementation while following it along, not that it is any complicated matter. The <em>c</em> start with a value of zero, when the algorithm iterates over the string of digits <em>c</em> is both input to the <em>d(j,k)</em> function (the <em>j</em> value) and the output replacing the previous or default value. Thus, in the Wikipedia example, previous <em>c</em> represent the <em>c</em> value from the previous iteration or the default value on the first iteration. For the benefit of all, I’ve realized that I could post my reply here as well:

You asked about where the previous c value came from. I guess it is easier to follow the example on Wikipedia if you take a look at my PHP implementation while following it along, not that it is any complicated matter. The c start with a value of zero, when the algorithm iterates over the string of digits c is both input to the d(j,k) function (the j value) and the output replacing the previous or default value. Thus, in the Wikipedia example, previous c represent the c value from the previous iteration or the default value on the first iteration.

]]> By: ANTHONY http://en.dahnielson.com/2006/09/verhoeff.html#comment-1656 ANTHONY Mon, 12 Feb 2007 08:56:47 +0000 http://en.dahnielson.com/2006/09/verhoeff.html#comment-1656 IVE BEEN READING WIKIPEDIAS EXPLANATION OF TH VERHOEFF SCHEME. but when it comes to their example am not able to figure out where they get the values for the column titled previous c. please help me on this. send expalnation to my email. IVE BEEN READING WIKIPEDIAS EXPLANATION OF TH VERHOEFF SCHEME. but when it comes to their example am not able to figure out where they get the values for the column titled previous c. please help me on this. send expalnation to my email.

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