Which of the following are part of a symmetric cryptosystems (private key cryptosystems)?
- $E_k(x) = x + k \bmod p$, where $x, k \in \Z_p$, and $p$ is a prime number.
- $E_{(a, b)}(x) = ax + b \bmod p$, where $a, b, x, \in \Z_p$, and $p$ is a prime number.
- $E_k(x) = (x+k)^2 \bmod p$, where $a, b, x, \in \Z_p$, and $p$ is a prime number.
- $E_k(x) = \text{AES}_k(x)$, where $x, k \in \Z_2^{128}$, and $\text{AES}_k$ is the AES encryption function with key $k$.
- $E_k(x) = \text{AES}_k(x) \oplus x$, where $x, k \in \Z_2^{128}$, and $\text{AES}_k$ is the AES encryption function with key $k$.
- $E_k(x) = \text{AES}_x(k)$, where $x, k \in \Z_2^{128}$.
- RSA
- ElGamal
If all encryption function $(E_k)_{k\in \mathcal{K}}$ are bijections, does it imply that any cryptosystem based on them is a symmetric cryptosystem?
Submit the answer as a sequence like 1 2 3 yes.