Key Hierarchy and key Encryption If i have two 56-bit DES keys, and I use these two key to encrypt a 256-bit AES key. Like this $K_{AT}$ encrypts $K_{BT}$ and $K_{BT}$ encrypts $K$

What is the effective security of key $K$?

Is it $2 \times 56$ bits?

Can anyone help?
The security - assuming you can validate the correctness of $K$ - is 56 bits (not even counting any attacks on DES itself, assuming to test all keys). This is because you can brute force $K_{BT}$ without even looking at $K_{AT}$ in your particular scheme.

[EDIT] I'll explain: lets assume that the correctness of the AES key $K$ can be verified by looking at known plaintext / ciphertext pairs. Knowing $K_{BT}$ unlocks the key $K$, which can then be verified. Hence brute forcing $K_{BT}$ is enough to find the right $K$. And $K_{BT}$ has a security level of 56 bits. You can completely ignore $K_{AT}$, it doesn't offer any additional security at all. Minor note: this will cost you at least 5 decrypts (4 DES encrypts or decrypts for retrieving the AES key and one AES encrypt or decrypt to verify correctness).

2 key triple DES on the other hand would at least offer over 80 bit security. So this scheme is certainly not the best option available if you have 112 bits of entropy for your key.