checksum algorithm

[gaf at blu.org (Jerry Feldman)]

Different credit cards have different check digit algorithms. The mod 10 
algorithm is in wide use because it is used by banks for account 
numbers and other numbers on your check. These work well with a small 
number of decimal digits. When you have a larger number of characters, 
sich as a packet, or a message, then a CRC algorithm is a better 
choice.  
On 14 Dec 2000, at 9:05, Ron Peterson wrote:

> 
> I'm interested in implementing a checksum algorithm to help reduce the
> probability of data entry errors in a database.
> 
> I took a stab at rolling my own, as follows:
> 
> //   0 1 2 3 4 5 6 7 (digit index)
> // * 2 3 4 5 6 7 8 9 (multiplier)
> //   - - - - - - - -
> //   x x x x x x x x => (sum(x)+checksum digit) mod 10 must be zero.
> //
> // This means that each of the first eight digits of the code - excluding
> // the check digit itself - is multiplied by a number ranging from 9 to
> // 2 and that the resulting sum of the products, plus the check digit,
> // must be divisible by 10 without a remainder.
> //
> // This algorithm is adapted from the checksum used for ISBN codes.
> // See http://www.isbn.spk-berlin.de/html/userman/usm4.htm.
> 
> Does this make sense?  This seems like it could be one of those areas
> where apparent simplicity belies deeper mathematical principals.
> 
> The criteria for this algorithm is that I end up with a nine-digit
> numeric code.  This seems to eliminate CRC or MD5, because they assume
> full use of the bit string.  Although I suppose you could just pick what
> you want out of the result.  I just wonder if there's any design
> advantage then, however.
> 
> I've looked at the credit card algorithm also.  It works according to
> a similar principal as the one above.
> 
> Ideally the algorithm would be particularly adept at detecting the
> most common typographical mistakes, such as transposed digits, off by
> one digit, etc.
> 
> Any comments?
> 
> -Ron-
> 
> -
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Jerry Feldman <gaf at blu.org>
Associate Director
Boston Linux and Unix user group
http://www.blu.org
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