Any protocol allowing multiple signature schemes needs to authenticate the choice of signature
scheme, so that signatures under one scheme cannot be confused with signatures under another.
For example, if a public key A were allowed to be used with both PureEdDSA and H -EdDSA
then an attacker could forge a signature of M under H -EdDSA by obtaining a signature of H (M )
under PureEdDSA. There are many other “cross-protocol” attacks in the literature; it is an error
to simply certify a public key A without also certifying the signature scheme to be used for A.