Consider the following variations on a Diffie$-$Hellman exchange, where Alice and Bob establish a shared key and carry on a conversation. Which security vulnerabilities does each of the following protocols have? Assume in the variants using public keys $($protocols $2-6),$ that Alice and Bob each have public$/$private key pairs and they know each other$$s public keys. In the variants using a pre$-$shared secret $($protocols $7-8),$ assume there is some secret KAB that both Alice and Bob know. Assume Trudy can be an active MITM $($for instance, she is malware on a router on the path between Alice and Bob$).$

Security vulnerabilities:

Trudy can impersonate Alice to Bob

Trudy can impersonate Bob to Alice

Trudy can be an active Meddler$-$In$-$The$-$Middle and see what Alice and Bob are saying to one another

Trudy can passively eavesdrop on the conversation and see what Alice and Bob are saying to one another

Protocols:

Alice and Bob each send their Diffie$-$Hellman numbers to one another $($Alice sends gA mod p$,$ and Bob sends gB mod p$)$ and then they encrypt their conversation with the Diffie$-$Hellman shared key.

Like $1,$ but Alice and Bob each sign their Diffie$-$Hellman numbers with their private keys and they each verify the other$$s signature knowing the other$$s public key. In other words, Alice sends $[$gA mod p$]$Alice$,$ and Bob sends $[$gB mod p$]$Bob$.$

Like $1,$ but Alice and Bob each encrypt their Diffie$-$Hellman numbers using the other$$s public key. In other words, Alice sends $\{$gA mod p$\}$Bob$,$ and Bob sends $\{$gB mod p$\}$Alice$.$

Like $1,$ but Alice encrypts her Diffie$-$Hellman number with Bob$$s public key. In other words, Alice sends $\{$gA mod p$\}$Bob$,$ and Bob sends gB mod p$.$

Like $1,$ but Alice encrypts her Diffie$-$Hellman number with Bob$$s public key and signs it with her private key. In other words, Alice sends $[\{$gA mod p$\}$Bob$]$Alice$,$ and Bob sends gB mod p$.$

Like $1,$ but Alice encrypts her Diffie$-$Hellman number with Bob$$s public key and Bob signs his Diffie$-$Hellman number with his private key. In other words, Alice sends $\{$gA mod p$\}$Bob$,$ and Bob sends $[$gB mod p$]$Bob$.$

Like $1,$ but Alice and Bob compute a conversation key by hashing together the Diffie$-$Hellman shared key and a secret they have both agreed to in advance. In other words, Alice and Bob use h$($S$,$ gAB mod p$)$ as their conversation key.

Like $1,$ but only Alice encrypts her Diffie$-$Hellman number with the secret S that she and Bob share. In other words, Alice sends $\{$gA mod p$\}$S$,$ and Bob sends gB mod p$.$