Mail exchange software

I need to allow users of my site to write emails to each other, without revealing their email addresses.

Here’s an example: user1@gmail.com sends an email to user2-alias@mydomain.com, user2@gmail.com receives it as sent by user1-alias@mydomain.com

I can do this with a process which checks the user1-alias@mydomain.com, modifies the email addresses of sender and recipient accordingly and forwards the email to user2@gmail.com.

But I’d like to know if there are other easier ways to do it. I tried with postfix forwarding, but couldn’t get to get both addresses translated.

Any ideas?