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hi Everyone please correct me if im wrong for my understanding for the man in the middle attack used in a variant of diffie hellman key exchange .

am i right to say that a protocol is susceptible to the man in the middle attack, if each participants is having their own private key of yP and public key of g^yP mod p and

A -> B : g^rA mod P

B -> A : g^rB mod P

rA and rB are random values each session and my shared key is = g^rAxB + g^rBxA mod P. This can be attack because the protocol does not authenticate participants .

am i right for that understanding ? and an adversary can just participate in that key exchange ?

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If there is no authentication of at least party then then no connection can be trusted, and MitM is possible. MitM does of course require an active attack; just eavesdropping is not enough, and unauthenticated DH does protect against eavesdropping attacks.

Note that the authentication may require a relatively low amount of data (e.g. there are protocols that simply use vicinity) but some kind of authentication does need to take place.

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