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2

I believe that you misunderstand what DH is doing. DH-key-exchange was innovated to defence man-in-the-middle attack, because hackers can not pretend the one you want to communicate without correct share key? or hacker don't know the key generator that Alice and Bob pre-agreed? Well, no, defending against active attackers, that is, attackers who can ...

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Yes for sure you can do that. Mapping this protocol to an elliptic curve setting is just like mapping DH key exchange to ECDH key exchange. In AugPAKE you work in a prime order $q$ subgroup of $Z_p^*$ and in the EC setting you use a prime order $q$ elliptic curve group. Observe that in the EC setting a multiplication of group elements in AugPAKE is then ...

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No, IKEv2 has nothing analogous to 'main mode' and 'aggressive mode', and they eliminated the initial 'quick mode', When IKEv1 was originally written, they wanted a strong separation between IKE and IPSec; they had a vision where IKE might be used for things other than IPSec (other "Domains of Interpretation"). So, they completely isolated the "negotiate ...

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