Crypto Protocols

1.Suppose Alice and Bob have obtained each other's public keys securely. I wrote a key agreement protocol that enables Alice and Bob to agree on a session key over an insecure communication channel that fresh and authenticated to be only available to Alice and Bob. Please help me figure out if my answer is correct:

Message 1: A → B:A,B, {NA1,A}KB +

A asks B for a session key for A and B to use. The message is encrypted by B's public key KA + Only B can decrypt this message with B's secret key KB −.

Message 2: B → A: B,A,{NA1,KAB,B}KA +

B returns a message encrypted by A's public key KA + for A that includes the session key.

Message 3: A → B: A,B,{NA2,}KAB

A decrypts message 2 to get KAB. A asks B to demonstrate knowledge of KAB through a nonce identifier for the transaction, NA2.

Message 4: B → A: B,A,{NA2 − 1}KAB

B decrypts message 3 and say one less to send a related reply to A.

2. Suppose Alice and Bob each share a symmetric key obtained securely. I wrote a key agreement protocol that enables Alice and Bob to agree on a session key over an insecure communication channel that fresh and authenticated to be only available to Alice and Bob. Please help me figure out if my answer is correct:

Message 1: A → B:A,B, {NA1,A}K

A asks B for a session key for A and B to use. The message is encrypted by symmetric key K.

Message 2: B → A: B,A,{NA1,KAB,B}K

B returns a message encrypted by

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