DSSA/SPX is the authentication protocol of DSSA. The CDC is a certificate granting server while the certificate is a ticket signed by CA which contains the public key of the party being certified. Since the CDC is merely distributing previously signed certificates, it is not necessary for it to be trusted.
A → C D C : B {\displaystyle A\to CDC\colon B}
C D C → A : certificate ( B , C A ) {\displaystyle CDC\to A\colon \operatorname {certificate} (B,CA)}
A → B : A , { T A , A } K A B , { L , A , P A ′ } S A , { { K A B } P B } S A ′ {\displaystyle A\to B\colon A,\{T_{A},A\}K_{AB},\{L,A,P'_{A}\}S_{A},\{\{K_{AB}\}P_{B}\}S'_{A}}
B → C D C : A {\displaystyle B\to CDC\colon A}
C D C → B : certificate ( A , C A ) {\displaystyle CDC\to B\colon \operatorname {certificate} (A,CA)}
B → A : { T A + 1 } K A B {\displaystyle B\to A\colon \{T_{A}+1\}K_{AB}}