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?