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From: mtonkin@gdwb.vic.gov.au (Malcolm Tonkin)
Newsgroups: sci.crypt
Subject: Self check algorithms - Pro's, Con's & How ?
Date: 18 Mar 1994 08:18:54 +1000
Organization: Barwon Water
Lines: 184
Distribution: world
Message-ID: <2mal0e$vc@thursday.isd.gdwb.vic.gov.au>
NNTP-Posting-Host: thursday.isd.gdwb.vic.gov.au

Firstly let me say that I am not a mathematician. I am a
computer analyst. I am also relatively new to this group and as
yet have not seen any discussion about my request........

I am looking for your advice on self check algorithms for
assigning suffix check digits to reference numbers such as
"Customer numbers" or "Account numbers" and the relative merits
of possible algorithms.

Our reasons for using them and the algorithms that we currently
use are set out below.

We are now finalising a functional requirements specification to
replace our existing IBM (System/38) based Customer Billing
system with a Unix / Ingres solution to run on a network of Sun
workstations and servers.

Hence we have an opportunity to review our methods.

I would appreciate your thoughts to be either posted to this
group, or to be emailed to myself in which case I will post a
summary of replies.

Thanks in anticipation,

Malcolm Tonkin.



Why we use them:
----------------

Within our Customer Billing system we have for a number of years
been using the IBM modulus 10 and modulus 11 algorithms, with we
believe, a reasonable level of success in achieving:

      * Integrity of data provided from payment collection
	agencies that have no link to our own data base. When
	the agent's cashiers key in our reference number
	(including check digit) the agent's computer system
	ensures that it agrees with the algorithm.

      * By ensuring that our data base only contains reference
	numbers that include an integral valid check digit, we
	are able to reduce the risk of our own staff simply
	keying in a reference number incorrectly, getting a
	match in the data base and without due care processing a
	transaction against the wrong Customer.



IBM Modulus 10 self check algorithm
-----------------------------------


For each position in the base number, there is a weight factor.

Positions are counted from the rightmost digit (not including
the check digit).

The Modulus 10 weight factor is 2 for positions 1, 3, 5, ....,
31; it is 1 for positions 2, 4, 6, ....., 30 respectively.

To compute a Modulus 10 self check digit:

1.      Multiply the units position and every alternate position
	of the base number by 2.

2.      Add the digits in the products to the digits in the base
	number that were not multiplied.

3.      Subtract the sum from the next higher number ending in
	zero to get the self check digit.


For example:
	
	Base number				6   1   2   4   8

	Units position and every 		6       2       8
	alternate position

	Multiply by the weight factor, 2       x2      x2      x2

	Products			       12       4      16

	Digits not multiplied                       1       4

	Add the digits of the products 		1 + 2 + 4 + 1 + 6 +
	and the digits from the base number     1 + 4 = 19
	not used for multiplication		

	Next higher number ending in 0		20
	
	Subtract				-19

	Self check digit			1


	The reference number becomes		612481


IBM Modulus 11 self check algorithm
-----------------------------------

For each position in the base number, there is a weight factor.

Positions are counted from the rightmost digit (not including
the check digit).

The Modulus 11 weight factors are 2, 3, 4, 5, 6, 7, 2, 3, 4, 5,
6, 7, ...2, 3, 4, 5, 6, 7, 2 for positions 1, 2, .... 31
respectively.

To compute a Modulus 11 self check digit:

1.      Assign a weight factor to each digit position of the
	base number.
	These factors are: 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7,
	2, 3, ...  starting with the units position of the
	number an progressing toward the high-order digit. For
	example, the base number 991246351 would be assigned the
	weight factor as follows:

	Base number     9 9 1 2 4 6 3 5 1

	Weight factors  4 3 2 7 6 5 4 3 2


2.      Multiply each digit by its weight factor.

3.	Add the products.

4.	Divide the sum by 11

5.	Subtract the remainder from 11.

The difference is the self check digit.


For example:

	Base number                     1  3  7  3  9

	Weight factors                  x6 x5 x4 x3 x2

	Multiply each digit by 
	its weight factor                6 15 28  9 18

	Add the products             6 + 15 + 28 + 9 + 18 = 76

	Divide the sum by 11         76/11 = 6 plus a remainder
						of 10

	Subtract the remainder from 11     11 - 10 = 1

	Self check digit                1

	The reference number becomes		137391



Note: If the remainder in step 4 is zero, the self check digit
is zero. If the remainder is 1, the base number has no self
check digit; you must make sure that such base numbers are not
used.



Pro' & Con's:
-------------

Mod 10  -       Can assign a numeric self check digit to any
		existing number.

Mod 11  -       Cannot assign a numeric self check digit to any
		existing number.


-- 
Malcolm Tonkin           		Malcolm.Tonkin@BarwonWater.Vic.Gov.Au
Information Systems, Barwon Water	Phone: +61 52 262541
61-67 Ryrie St Geelong 3220 Australia  	Fax:   +61 52 218236