Strong naming is not intended to provide authenticity, validation, protection, or anything else like that. Its sole purpose is to provide a unique ID to an assembly or series of assemblies. This is so that you can have many assemblies named "Library" in the GAC, and when your application asks the runtime to load "Library", the system knows this means your "Library" assembly and not someone else's.
In light of this, I would simply include the strong name key in the source tree. If for some reason your project wants to provide authenticity or any of those other things, then you probably want Authenticode signing, which is not free and really is probably unnecessary for an open source project. If you decide to go that route and are wondering who should own the code signing key, that becomes more of a political question.