Does NTRU provide Perfect Forward Secrecy? Does NTRU provide Perfect Forward Secrecy if the world would use it in an HTTPS connection?
Properly speaking, forward secrecy is a property of a protocol. The protocol is forward secret if compromise of the long term keys does not allow an attacker to decipher any past communications.

(Occasionally a distinction is made between that and perfect forward secrecy, with the latter secure when the attacker also knows e.g. all other session keys.)

You can build a key exchange protocol that provides forward secrecy from any authenticated public key encryption, including NTRU:


Assume the parties have exchanged long term keys.
A generates an ephemeral key-pair and sends the public key to B, using the long term keys for authentication.
B generates a session key, encrypts it for A's ephemeral keys and sends it to A.
A deletes the ephemeral key-pair after decrypting the session key.




However, if you mean the old draft protocol I linked in a previous answer, then, no. Unless I'm missing something, that protocol just encrypts a random secret using the long term keys. That does not provide forward secrecy.