Reverse engineering a check digit algorithm

Question

I am trying to reverse engineer an algorithm used to generate a check digit.

Numbers are 8 digits long and the last digit is the check digit. I have thousands of valid numbers to test it on.

I have tried a standard Luhn, Verhoeff and modulo-10 algorithms (brute force checking of all possible weights), but could not find an answer!

Is it possible to calculate this? Any ideas?

Here is some examples of valid numbers:

1002784-5
1000514-7
1001602-8
1001255-2
1001707-1
1003355-5
1005579-1
1004535-0
1004273-1
1001695-9
1004565-9
1000541-9
1001291-1
1005866-1
1004352-7

EDIT: Thanks guys - I don't have access to the code unfortunately. The number is a tax number, I need to be able to verify that the number was typed in correctly. From my research is looks like most countries use a pretty standard modulo-10 type system. I've got access to about 60 000 numbers.

I understand that the problem could be impossible to solve, it was more of academic concern.

Answer 1

First check your context:

If context is credit cards, driver's licenses, government licensing numbers (not SSN) think Luhn or Mod 10. If some other industry, does that industry have a defacto standard? If not, is the developer of the system using the numbers also a player in an industry that has a de facto standard?

Nobody likes to reinvent the wheel if they don't have to.

If that doesn't help keep in mind:

Don't assume that all the numbers in the keys you are testing against are used to arrive at the check digit. It's possible only 4 or the 8 digits are being used to calculate the check digit (or any other combination). It's also possible there is some external PREFIX number that is used with the other digits to arrive at the check digit. So... line up all your numbers with the same check digit, and see what the similarities are. Can you add a number to them and then always reach check digit? Can you test only the first few digits? Last few digits? every other digit?

Good luck.