Suppose N many messages has been sent from A to B in this format:

• HMAC(K, C(i)) || C(i).

Where

• C(i) is some cipher-text encrypted with some secure algorithm using some key
• K(i) != K for any i in range [0, N-1].

There is no implication whether K(i) = K(j) for any i != j.

Thus, it is just "some" encryption algorithm but encryption key used to encrypt the message is not directly equal to K, the key for HMAC which is constant for each N messages.

Now my question is:

If the attacker captures these N messages and HMAC's, does it give any more advantage to the attacker than just "brute-forcing" the key K to find it (whether he can draw some conclusions, etc)? We can say that the cryptographic hash function used in the HMAC is secure.

Suppose $N$ many messages has been sent from $A$ to $B$ in this format:

• $\operatorname{HMAC}(K, C(i)) \mathbin\| C(i)$.

Where

• $C(i)$ is some cipher-text encrypted with some secure algorithm using some key
• $K(i) \ne K$ for any $i$ in range $[0, N-1]$.

There is no implication whether $K(i) = K(j)$ for any $i \ne j$.

Thus, it is just "some" encryption algorithm but encryption key used to encrypt the message is not directly equal to $K$, the key for HMAC which is constant for each $N$ messages.

Now my question is:

If the attacker captures these $N$ messages and $\operatorname{HMAC}$s, does it give any more advantage to the attacker than just "brute-forcing" the key $K$ to find it (whether he can draw some conclusions, etc)? We can say that the cryptographic hash function used in the $\operatorname{HMAC}$ is secure.

Suppose N many messages has been sent from A to B in this format:

• HMAC(K, C(i)) || C(i).

Where C(i) is some cipher-text encrypted with some secure algorithm using some key K(i) != K for any i in range [0, N-1].

There is no implication whether K(i) = K(j) for any i != j.

Thus, it is just "some" encryption algorithm but encryption key used to encrypt the message is not directly equal to K, the key for HMAC which is constant for each N messages.

Now my question is:

If the attacker captures these N messages and HMAC's, does it give any more advantage to the attacker than just "brute-forcing" the key K to find it (whether he can draw some conclusions, etc)? We can say that the cryptographic hash function used in the HMAC is secure.

Suppose N many messages has been sent from A to B in this format:

• HMAC(K, C(i)) || C(i).

Where

• C(i) is some cipher-text encrypted with some secure algorithm using some key
• K(i) != K for any i in range [0, N-1].

There is no implication whether K(i) = K(j) for any i != j.

Thus, it is just "some" encryption algorithm but encryption key used to encrypt the message is not directly equal to K, the key for HMAC which is constant for each N messages.

Now my question is:

If the attacker captures these N messages and HMAC's, does it give any more advantage to the attacker than just "brute-forcing" the key K to find it (whether he can draw some conclusions, etc)? We can say that the cryptographic hash function used in the HMAC is secure.