The "one shot" symmetric key is purely random.

No it's not a function of anyone's private or public key.

Once generated, it is encrypted using the public key of the recipient and
included with the message.  If multiple recipients, the same key is used to
encrypt the data, and for each recipient it is encrypted under that
recipients public key and included as part of the message.

The private key used to decrypt is the one that matches the public key that
was used to encrypt the symmetric key.  (i.e. HIS private key).

Dave


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