Doubling the block length of a given block cipher
Parallel construction


Then my first feeling is that you wouldn't lose that much in security however there are several drawbacks.


you would be basically having a kind of ECB inside your $2n$-block-cipher.
you do not have a full diffusion on your $2n$-block-cipher : if you change a bit in the first part, only that part is modified (orange diffusion on red).





$2n$-Feistel construction

However if you meant to use that $n$-block-cipher as $F$ in your Feistel $2n$-block-cipher, then you will have to make a sufficient number of rounds (at least 4 to get full diffusion : see p. 41). Therefore compared to a parallel CTR encryption method just using that $n$-block-cipher, you are 4 times slower and you don't really have a gain in security in term of key as the space is the same.

Your idea is this : given a $n$-bit block cipher, one can construct a $2n$ bit block cipher using a Feistel construction. More over you want to use 2 keys in order to increase the security margin.



Given enough rounds (at least 4), I can't see any security hole in that construction (but I'm not a cryptographer yet).



$m$-blocks Feistel construction ($m \times n$ bits-block-cipher)

for i in [1 .. number_of_rounds] do
    for j in [1 .. m] do
        subblock[j+1 mod m] ^= E(K[j],subblock[j])


This construction can be displayed as such (e.g. with 5 blocks, 2 rounds)



In order to get a full diffusion you need a strict minimum of 2 rounds.
However this is the same as using the $n$-cipher as a keyed $S-box$. By the way, the more blocks you add, the closer you are to a SPN.