Combining cascaded encryption keys into one key
For a crypto algorithm that acts like a group, the first thing that comes to mind is Pohlig-Hellman.  In this method, we have a large prime $p$, and define:

$$E_A(Data) = Data^A \bmod p$$

(with $A$ relatively prime to $p-1$)

This has the property that $E_B(E_A(Data)) = E_{A \times B \bmod p-1}(Data)$; however it has the security properties you're looking for; for example, given lots of $X, E_A(X)$ pairs, you can't recover $A$.

Now, this is a symmetric system (given $A$ and $E_A(Data)$, you can recover $Data$).  If you insist on an asymmetrical system, you might want to do this modulo a composite of secret factorization; only some who knows the factorization can then decrypt.  That version might be somewhat related to a better known asymmetric scheme...