Can double-encrypting be easier to break then either algorithm on its own? As was pointed out in Martin Bonner's comment I cannot prove this, but it seems intuitively impossible.

An encryption function is supposed to obscure the plaintext to the point where no information can be obtained about it. If the underlying encryption algorithm can even be determined, that goal has not been achieved.

Is this correct? Can double-encrypting (with either the same or separate algorithms) weaken security?
Can double-encrypting (with either the same or separate algorithms) weaken security?


If you do not assume that the algorithms and keys are independent, then it certainly can.

The example of ROT13 from the other answer illustrates the point even if it is not real encryption. Similarly, a synchronous stream cipher applied twice with the same key will undo itself. Something like that could be possible with other kinds of ciphers, e.g. you could have block cipher such that $E_k = D_{k'}$ if you choose the keys wrong, or you could define AES' where the encrypt and decrypt directions are switched. A combination of these would be secure with independent keys but not necessarily otherwise.

If you assume keys are independent, the result can still be weaker compared to the stronger of the two algorithms. For example, assume you have CBC encryption that is vulnerable to a padding oracle attack. Even if you add a secure stream cipher on top, the padding oracle attack still exists. With some of those assumptions you can say that the combination is no weaker than the first cipher (pdf).