My hashing algorithm computes the SHA-256 for each of 12 input strings and XORs them to get the final hash.
Is there a risk of an attacker being able to forge 2 sets of inputs that yield the same final hash?
To avoid trivial attacks by feeding in the same input twice and make this scheme order-dependent, I prepend each input with its index (binary 0 to 11).
For the case of 256 inputs there is an easy attack (as each hash can be used to control a single output bit using matrix calculus), this makes me wonder whether there are similar attacks for just 12 inputs.
I'm aware that there are more secure alternatives such as Merkle trees but I really need maximum performance especially for when just a single input is modified.