One-way Functions for Floating Points
This would appear to be impossible.

You require that $|x_1 - x_2| &lt; \epsilon$ implies that $|f(f(x_a, k_a), k_b) - f(f(x_b, k_b), k_a)|&lt;\delta$ ; this implies that $f(f(x_a, k_a), k_b)$ is continuous over $x_a$.

Now Charlie knows $k_a, k_b$ and can compute the target value $f(f(x_a, k_a), k_b)$; a simple bisection search over the function $f(f(x, k_a), k_b)$ would allow him to recover $x_a$ (or at least, a good approximation).