If I split a key $k$ into three pieces as $k1, k2$ and $k3$ how should I distribute the keys among three people such that any two of them are able to evaluate PRF, but be secure from any one of them trying to do so. The PRF is defined as
It is known that the three people know what pieces they hold so in this case if I split the keys in pair as $k1, k2$ for first person, $(k1, k3)$ for second and $(k2, k3)$ for thrid person and compute
$F1((k1, k2), x) = F(k1, x) ⊕ F(k2, x)$
Now if I send this $F1$ to the second person and compute $F1 ⊕ F2$ where $F2$ is given as below then I should be able to recover the PRF $F'$. Is that correct?
$F2(k3, x) = F(k3, x)$