$($Apu $,$ Apr$)$ and $($Bpu $,$ Bpr$)$ are, respectively, Alice's and Bob's $($public$,$ private$)$ key pairs used for message signing. Which $($if any$)$ is a correct way to use these keys to respond to a challenge C$,$ issued by Bob, to authenticate Alice?

Group of answer choices

Apu$($C$)$

Apr$($C$)$

Bpu$($C$)$