Encryption using two keys Suppose we have two secret keys K1 and K2, I'd like to ask if there is any encryption scheme that allows us to derive another key K12 from K1, and K2 and for a message x, EK12(x) = EK1(EK2(x)).

EK(x) is the encrypted text of x using key K.
Yes, it is possible with a symmetric system.

One way would be if we had a public prime $p$, and secret keys $k_1, k_2$ which are values relatively prime to $p-1$.

And, we define $E_k(M) = M^k \bmod p$; decryption then is $D_k(M) = M^{k^{-1} \bmod p-1} \bmod p$ (the value $k^{-1} \bmod p-1$ is easy to compute, given $k$).

And, for $K_{12} = K_1 \cdot K_2 \bmod p-1$, we have $E_{K_{12}}(M) = E_{K_1}(E_{K_2}(M))$