I have already read Using Java to encrypt integers and Encrypting with DES Using a Pass Phrase.
All I need is a simple Encrypter which transforms a 12 digit number t
If the strict 1:1 mapping is more important than protecting against cryptanalysis, then you can convert the password to a 12-digit number (via hash or otherwise) and simply add to your original number mod 10^12. If you absolutely must remove leading zeros from the output, you can subtract 10^11, do the math mod (10^12 - 10^11), and then add 10^11 back again. Granted, that's extremely insecure, but it's quite simple. :)
If the range of inputs is bounded by a prime less than (10^12 - 10^11), you may be able to use message ^ password mod prime to form a ring that will satisfy your requirements and be a little harder to crack. (This is similar to how RSA works.) I think this could work if you don't need to decrypt it.
I agree with Jon Skeet: requiring a strict 1:1 mapping without the output range being bigger than the input domain is something that most encryption libraries are not going to handle.