Block Ciphers / Kerckhoffs Principle I am newbie to the crypto world, but my question is, If block cipher BLOCK satisfies the following relation (where ENC is encrypt and "+" means XOR): For ever pair of blocks of input A and B, ENC(A+B) = ENC(A) + ENC(B). 

I was wondering what would be the security of BLOCK? Assuming the key is of fixed size and that you have unfetterd access to the ENC function. In other words, how hard is it to decrypt a given ciphertext without knowing the details of BLOCK.
In other words, how hard is it to decrypt a given ciphertext without knowing the details of BLOCK.


Pretty easy; all you'd need to do is ask for:

ENC(0x000..0001)
ENC(0x000..0002)
ENC(0x000..0004)
ENC(0x000..0008)
ENC(0x000..0010)
...
ENC(0x400..0000)
ENC(0x800..0000)


For an $n$-bit block cipher, that's $n$ queries.

Then, you find the linear combination of the above values that gives you the known value ENC(BLOCK) (for example, by Gaussian Elimination); by the homomorphic property you listed, that immediately gives you the value of BLOCK

This same strategy can be devised as a known ciphertext attack, using $n+\epsilon$ random known plaintexts, that'll allow you to decrypt any ciphertext with high probability.