There are three typical ways to use nonces as challenges. Suppose Na is a nonce generated by A$,$ A and $B$ share key $K,$ and $f()$ is a function $($such as increment$).$ The three usages are

$\backslash$table$[[$Usage $1,$Usage $2,$Usage $3],[(1)AB$:$Na,(1)AB$:$E(K,Na),(1)AB$:$E(K,Na)$