Can I ask for first authorship on future publications that may come out of my design? I am working on a 2-phase design. The first phase is where ideas are proved and verified. The second phase is an implementation of the first stage (Basically, like having a schematic of a building and actually building it). I have done lots of work on the first phase. My supervisor is asking me to give the final work to another person, who we don't yet know who he is, for implementation and work on something else. While my advisor has some contribution, I did almost everything. 

Can I ask for first authorship for any papers and publications that come out of this now?
Generally speaking, you cannot "reserve" first authorship on possible papers that may come out of some work that you've done. Depending on the scope of the submission (when it's completed) and who writes/edits the actual text of the paper, you may or may not actually deserve first authorship on it. It would be inappropriate to promise you first authorship on all future papers coming out of the design at this stage. 

What you can do is tell your advisor, 


  I'd like to start working now on a draft of a paper about my design.


Discuss the planned scope of your submission with your advisor: in particular, whether your paper should include a description of the implementation which has yet to be done, or whether a paper on the design alone is sufficiently publishable. Either way, start working on a draft right away.

Also discuss authorship of the paper you're going to start writing, given the scope the two of you have agreed on for this particular paper, including:


whether you will be first author
whether your advisor will be a co-author
what position the other yet-to-be-named implementer will have (if you decide to include the implementation in the paper)
and what additional contributions are expected from each author in order to merit authorship according to this agreement (both technical, and with respect to writing and editing).  


If you discuss this with your advisor, start working on a draft now, write a lot of the text in the submission, and you generally "drive" the project and the paper submission forward, you will (assuming your work meets the standards for first authorship in your field) have a very strong case for first authorship on this paper.

Note that unless you do more work to merit authorship on other, future papers related to your design, they'll only be expected to cite and/or acknowledge your work.