In general I would love to see a good work of fiction based on Bitcoin. However, OP, I think you should really investigate a bit more in depth, because even if franky1 has already answered your question well, for a good work a more complete understanding would be needed than only the private key format (and perhaps some blockchain basics). The
Bitcoin Wiki has some good information in small chunks which may not be immediately accessible but also not too difficult. I would suggest at least some more months of investigation.
As suggestions for narratives: First, I think many Bitcoiners would appreciate if you don't try to guess Satoshi's physical appearance (gender, age, nationality etc.). So I'd suggest not to use Satoshi as the main character but as some mysterious figure in the background. Second, if the narrative is driven by some Bitcoin-technology related issue (e.g. how a group of people benefitted from the P2P nature ...) then it would be much better than, for example, a simple crime or love story with some Bitcoin technobabble in the background. This is also the reason why you should really investigate well, to understand how Bitcoin really achieves its advantages like censorship resistance and freedom of middlemen.