Earlier quoted context omitted.
We use scrypt for passwords hashing. This is modern hard to crack password hashing algorithm. We do have database access logs, so it was pretty straightforward to identify which users were affected.
Thanks for clarifying, good to see you're using a decent hashing algorithm :) I'm still a little unsure of how you are able to know some users had their password compromised. Is it a simple case of finding successful log in attempts from the same IP address as attack?
This is how we define "compromised" - people which had their passwords hash with old algorithm, which is relatively easy to crack.