Same problem as for document signatures, one needs a trustworthy timestamping service certifying the time of signature, so the client may check if the whole cer

Same problem as for document signatures, one needs a trustworthy timestamping service certifying the time of signature, so the client may check if the whole certificate chain might have been valid at the time. This means that you need far more extensive CA and revocation databases than for TLS, because you need to keep all that historical data.