Topic summary
Preimage resistance
Extracted from the Wikipedia article Preimage attack.
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.