Australia’s about as sparsely populated …
Sorry what? Australia’s population density is is 3.6/km², the US’s is 33.6/km², almost 10 times higher. Even if you fudge it by treating the swathes of uninhabited desert as an outlier and ignoring them, you’re still dealing with a raw number of people lower than the population of Texas.
That’s just a one-time pad with extra steps.