Only if they're lazy and went with the "download key and certificate (and we'll generate the keys for you)" option. Otherwise at least how it's supposed to work is that you give a CA a certificate signing request (CSR) containing your public key, they sign it and hand back your certificate. The certificate itself doesn't contain anything sensitive, because it's the same thing that your server presents to clients. But people are lazy and might not know how to generate a csr locally, hence the aforementioned option. And of course if they're too lazy to generate a csr locally, they're probably also too lazy to keep backups, so you can be sure that eMudhra keeps a copy in case they deleted it from their downloads folder.
alt Hacker News
Only if they're lazy and went with the "download key and certificate (and we'll generate the keys for you)" option. Otherwise at least how it's supposed to work is that you give a CA a certificate signing request (CSR) containing your public key, they sign it and hand back your certificate. The certificate itself doesn't contain anything sensitive, because it's the same thing that your server presents to clients. But people are lazy and might not know how to generate a csr locally, hence the aforementioned option. And of course if they're too lazy to generate a csr locally, they're probably also too lazy to keep backups, so you can be sure that eMudhra keeps a copy in case they deleted it from their downloads folder.