I am currently working on the following task:
Let F be a pseudorandom permutation.
- Consider the encryption scheme for the message space $\{0, 1\}^n$ defined as follows: $Gen(1^n)$ chooses two random keys $k_1 , k_2 \in \{0, 1\}^n$. Encryption is done as $Enc_{k_1,k_2}(m) = F_{k1}( k_2 \oplus m)$ (Decryption is done in the natural way)
Does this scheme have indistinguishable encryptions in the presence of an eavesdropper? Is this scheme CPA-secure?
- Consider the encryption scheme where the message space is $\{0, 1\}^{n/2}$ and encryption of a message $m$ is done by choosing random $r \leftarrow \{0, 1\}^{n/2}$ , and then outputting the ciphertext $F_k(r ||m)$. (Decryption is done in the natural way)
Does this scheme have indistinguishable encryptions in the presence of an eavesdropper? Is this scheme CPA-secure?
My current answers are:
This scheme has indistinguishable encryptions in the presence of an eavesdropper since $F$ is a PRP, and therefore $F_{k1}( k_2 \oplus m)$ will give a pseudorandom string. However I am not sure whether my intuition is correct. The scheme should not be IND-CPA secure since encryption is deterministic.
This scheme is both IND-COA as well as IND-CPA secure. IND-COA since (as in 1.) $F$ is a PRP, and therefore $F_k(r ||m)$ will give a pseudorandom string. It's also IND-CPA secure as a random $r$ is used every time a message in encrypted.
Since I am not too confident about my solutions I appreciate any comments and/or corrections.