This is well beyond my understanding and I am hoping there is someone out there that can help. I have looked on the forum for an answer but this is a rather unique request.

We manufacture access control systems, part of which uses Mifare cards as access credentials. Our system reads the card serial number, which is 10 digits, and drop the two most significant bits to leave an 8 digit number that our system can read.

A potential customer with 300,000 staff is looking to implement these tokens with a new installation of our system but is in fear of seeing duplicate numbers within the 300,000 tokens issued.

This is how it works with our system:

The 32 bit Mifare Chip Serial Number is converted to a decimal 9/10 digit number. Net2 (the system) then drops the most significant digits to produce an 8 digit number.

A Mifare card with this CSN (serial number) 3125031963
Will display in Net2 (the system) as token 25031963

To add to this there is likely to be around 1000 independent systems installed.

My question is:

What is the probability of seeing a duplicate number amongst the 300,000 users? (Our internal teams have suggested that the figure is somewhere around 1 in 1 million, this sounds a little too convenient (1 in a million!)


What is the probability of seeing a duplicate number on a single system?

I hope that someone out there may be able to help me and I greatly appreciate any feedback provided.