I have been taking a look at ETSI TS 133 501 V16.3.0 to see how exactly does a User Equipment actually authenticates itself to the Home Network.
This is supposed to be done during the AKA procedure, but when I look at it, the HN is able to retrieve the SUPI from the SUCI without the UE having sent its ephemeral public key (section 6.1.2). Has the UE already sent its ephemeral public key before AKA takes place?
Also what seems odd to me is that in section 6.12.5, which talks about how to obtain the SUPI from the SUCI, nothing is said about the UE's ephemeral public key. However in annexe C, all protocols (except for the null one) are ECIES based and therefore HN needs to know UE's ephemeral public key.