Suppose a PKI hierarchy like below.
root CA ==> inter-1 CA ==> user-1
\
\======> inter-2 CA ==> user-2
My question is: does root CA also need to periodically download CRL from its children: inter-1 and inter-2?
Since user-1 and user-2 can authenticate each other, if user-2's certificate is revoked by inter-2, inter-2 should let root know and then propagate to inter-1 and user-1, right?
If so, it seems quite complicated. Is there any tool to use for managing the revocation logic? Thanks a lot.
No, revocation of certificate is not propagated across the CA tree. Each CA (root and intermediate in your case) is responsible of the publication of the CRL containing the list of only the revoked certificates that were issued by this CA.
An example:
Root CA publishes a CRL for the certificates issued by Root CA: inter-1 CA and inter-2 CA. Root CA is not aware of the user-1 and user-2 certificates or their revocation status.
inter-1 CA (resp inter-2 CA) publishes a CRL containing the list of revoked certificates issued by inter-1 CA (resp inter-2 CA) and only these certificates.
if user-1 certificate is revoked, this certificate (actually its serial number) will only appear in the CRL published by inter-1 CA.
When someone wants to check the validity the user-1 certificate the process is as follows:
Note that validating the CRL signature can trigger a validation of another certificate chain : i.e. this algorithm can be recursive. Actually the X.509 certificate validation algorithm is (very) complex and I just summarize the principles here.