which of the following is correct about the KDC$($key distribution center$)$

$$ a$.$ The KDC creates a permanent secret key for each member.

$$ b$.$ The KDC creates a permanent secret key and public key for each member.

$$ c$.$ To reduce the number of keys, each person establishes a shared secret key with the KDC$.$

$$ d$.$ The KDC$\text{'}$s purpose is to verify someone's public key to make sure it belongs to them