The Multi-user Security of Double Encryption
It is widely known that double encryption does not substantially increase the security of a block cipher. Indeed, the classical meet-in-the middle attack recovers the 2k-bit secret key at the cost of roughly \(2^k\) off-line enciphering operations, in addition to very few known plaintext-ciphertext pairs. Thus, essentially as efficiently as for the underlying cipher with a k-bit key.