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My guess is that when it is written approximately Can we really have a non-replayable 2-msg protocol? □ Remember (the question's protocol) insecurity the author is thinking about an attacker capturing the first message of the exchange $(A, g^x, \operatorname{SIG}_a((g^x, B)))$ and using a replay of that to impersonate Alice. There are two variants: ...
Let's call the problem Square Diffie-Hellman (SDH). SDH is at least as hard as CDH in groups of known order and the reduction goes as follows.$^*$ Given an adversary $\mathsf{A}$ that breaks SDH, our goal is to construct an adversary $\mathsf{A}'$ that breaks CDH. Given the CDH challenge $(g,g^x,g^y)$, $\mathsf{A}'$ runs $\mathsf{A}$ thrice -- first on $(g,g^... 6 This problem is equivalent to the CDH problem: Here is how to solve CDH given an Oracle that solves this problem: Given$g, g^x$, we can compute$g^{x^{-1}}$(which is equivalent to the CDH problem) by doing the following: Call the Oracle with$g, g^x$; the Oracle gives us a pair$g^{y}, xy$We compute$(g^{y})^{(xy)^{-1}} = g^{x^{-1}}$, hence showing one ... 5 Well, it's one less thing for the server to get wrong; I'll be giving my answer in the context of TLS 1.2 (as that was the context Mozilla assumed); remember, in TLS 1.2, it is the server that proposes the group, and Mozilla makes clients. A "randomly generated group"; there are a number of ways of generating such a group, and they vary both in ... 3 As far as my understanding of the ECDH goes, after systems are encrypted using ECDH protocol Stop right here, you cannot encrypt data using ECDH. ECDH is an algorithm, not a full fledged transport protocol (or protocol for securing data at rest, for that matter). Literature says that ECDH is used for the purpose of key exchange(when data is encrypted using ... 1 The process in the picture shows nothing about authentication You are correct in that explicit signatures are never sent, however the exchange involves so-called implicit signatures. You will note that the derivation of the shared secret relies not only on the ephemeral session keys$(x,X)$and$(y,Y)$, but also the long-term authentication keys$(a,A)$and ... 1 Theorem 1 is not true in general; consider a group where the discrete log problem is easy. On the other hand, it is true if we assume that the discrete log problem in$G$is hard (that is, if we can recover either$a$or$b$given$g^{b^{-1}}, ab$, then we can use that as an Oracle to recover$x$given$g^x$) Theorem 2 is true; for any$b \ne 0$(and we know ... 6 Are their values fixed for each DHE group ? Yes, by convention a named group includes at least$(g,\mathbb G,q)$with$\mathbb G$being a description of the group parameters (i.e.$(p,a,b)$for prime elliptic curves or$p$for FFDH),$g$being the generator and$q\$ being the generator's order. How do the communicating parties using Finite Field DHE agree ...