Preimage attack

In cryptography, a preimage attack on cryptographic hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its preimage (set of possible inputs). In the context of attack, there are two types of preimage resistance: preimage resistance: for essentially all pre-specified outputs, it is computationally infeasible to find any input that hashes to that output; i.e., given y, it is difficult to find an x such that h(x) = y. second-preimage resistance: for a specified input, it is computationally infeasible to find another input which produces the same output; i.e., given x, it is difficult to find a second input x′ ≠ x such that h(x) = h(x′). These can be compared with a collision resistance, in which it is computationally infeasible to find any two distinct inputs x, x′ that hash to the same output; i.e., such that h(x) = h(x′). Collision resistance implies second-preimage resistance, but does not guarantee preimage resistance. However, under certain assumptions of the range of the hash function, collision resistance does imply preimage resistance (by a provisional implication). Conversely, a second-preimage attack implies a collision attack (trivially, since, in addition to x′, x is already known right from the start). Via the provisional implication, a preimage attack will also imply a second-preimage attack, which then also extends to a collision attack.