Any Kerberos principal can authenticate to other principals within the same
Kerberos realm. However, it is also possible to configure a Kerberos realm
so principals in one realm can authenticate to principals in another realm.
This is called cross-realm authentication.

The way this is implemented is the KDCs in the two realms share a special
cross-realm secret, and this secret is used to prove the identity of
principals when crossing the boundary between realms.

Kerberos 5 supports an additional variant of this called transitive
cross-realm authentication. In traditional cross-realm authentication, each
pair of realms that wish to authenticate need to share a cross-realm secret.
This means in a group of N realms, 2 * ((N - 1) ** 2) secrets will need to
be exchanged in order to cover all possible cross-realm authentication
paths.

In transitive cross-realm authentication you can define a path of realms
connected via cross-realm secrets and use this path to "hop" between realms
until you get credentials in the desired realm.

Information on configuring cross-realm authentication can be found in the
answer to Question 2.15