## A function

*f*is*k-private*iff no finite set of argument-value pairs {(*x*1,*f*(*x*1)), …, (*x*n,*f*(*x*n))} suffices to compute*f*at any other point x {*x*1, …,*x*n}.## Example: a polynomial of degree exactly

*k*is*k*-private but not (*k*+1)-private## Wait. This depends on

__knowing__that*f*is a polynomial of degree*k*. That is__metadata__about*f*(semantics).## What kinds of metadata can we have about functions and what can be inferred from metadata?

## A function

*f*is*totally private*iff it is*k*-private for all*k*>0## Example: a general power series is totally private (without other metadata about

*p*(*x*))## In general,

*k*-privacy and total privacy are undecidable