# getting key $k_{2}$ somehow definitely compromise authentication scheme and attacker can see cipher text now...so not secure

I was going through this question of nested encryption:

Given $$\Pi$$ = $$({Gen}, {Enc}, {Dec})$$ is authentication encryption we have designed new scheme $$\Pi^{'}$$ = $$({Gen^{'}}, {Enc{'}}, {Dec{'}})$$ and which follows: $$\mathrm{Gen^{'}}(1^{n})$$ gives uniformly random keys $$(k_{1},k_{2}) = \{0,1\}^{n} \times \{0,1\}^{n}$$. And $$\mathrm{Enc^{'}}((k_{1},k_{2}),m)$$ =$$\mathrm{Enc^{'}}(k_{2}, \mathrm{Enc}(k_{1},m))$$ And deccryption algorithm $$\mathrm{Dec^{'}}((k_{1},k_{2}),m)$$ gives $$\mathrm{Dec^{}}(k_{1}, \mathrm{Dec}(k_{2},m))$$ if $$\mathrm{Dec}(k_{2},c) \ne \perp$$ else $$\perp$$ otherwise. Proof this is not authentication encryption if attacker gain access to $$k_{2}$$ but not $$k_{1}$$.

My intuition is getting key $$k_{2}$$ somehow definitely compromise authentication scheme and attacker can see cipher text now...so not secure but how to go towards formal proof.

getting key $$k_{2}$$ somehow definitely compromise authentication scheme and attacker can see cipher text now...so not secure

• What is the question here?
– tylo
Mar 24, 2021 at 7:25
• the question is how to formally proof if attacker gain access to k2 but not k1 this scheme defined $\Pi_{'}$ is not authenticated encryption. @tylo
– Sam
Mar 24, 2021 at 7:56
• This looks like a homework question. So you might first want to present what you tried so far and why it does not work. And the question should probably be more specific, because right now this looks to me like "do my homework for me".
– tylo
Mar 24, 2021 at 8:16
• "getting key k2 somehow definitely compromise authentication scheme and attacker can see cipher text now...so not secure" here you are mixing up concepts for confidentiality and integrity. The authentication part does not hide the message from the attacker. If you want to break the authentication part, then looking at ways for the attacker to break the encryption part is going the wrong way. Since this is explicitly authenticated encryption, the attack is very likely to target the authentication part.
– tylo
Mar 24, 2021 at 8:27
• @tylo i am presenting my intuition so that someone can guide me ...how to reach solution because i have no exposure to these king of question....but i am wondering why people like you is replying something absurd ....and i should say even in first post i have mention complete question ..you did not understand the question then and now also....so you are replying anything.....i request you if you do not know anything related to question please do not reply anything....
– Sam
Mar 24, 2021 at 8:28