can this apply to the real world in modern implementations of RSA?
RSA is a trapdoor function and the RSA public encryption/decryption and RSA signatures are derived from them. Contrary to some people, RSA decryption is not a signature.
RSA must never be used without proper padding. It is very dangerous and example attacks can be seen from the paper ...
No, X.509 cannot be used for symmetric cryptography directly. Inside the certificate is a public key of the subject of the certificate. The subject controls the private key.
The X.509 name is a reference to CCITT / ITU-T X.509; X.509 certificates are used as base of PKIX, the Public Key Infrastructure. PKIX is a tree structure where a Certificate Authority ...
There are two different identifiers in a certificate, the algorithm of the public key for the certificate and the algorithm of the signature from the issuer. The two don't have to even be the same algorithm family (e.g. RSA CA certs can sign ECDSA certs, and vice versa).
In the following certificate parse structure the algorithm identifiers starting at ...
The ASN.1 module
The OID of RSASSA-PSS is specified as below, however, it should only be used as part of an AlgorithmIdentifier, which is a SEQUENCE of the OID, followed by the parameters. These parameters are NULL for PKCS#1 v1.5 signatures, but for PSS they must be present
Here is the OID:
-- When id-RSASSA-PSS is used in an AlgorithmIdentifier,...
X.509 is just a standard to verify that a public key belongs to the user, computer or service identity contained within the certificate.
It has concretly nothing to do with symmetric-key algorithms, it just carries the information about the identity to which a certificate is issued and the identity that issued it.
The certificate is signed with the Certificate Authority's private key, but the purpose of an X.509 Public Key certificate is to associate a public key with a subject-entity.
You generate a public/private pair
You generate a PKCS#10 CSR which contains the SubjectPublicKeyInfo, signed with the private key as proof-of-possession.
You submit the PKCS#10 CSR to ...