Difficulty of finding an input string that hashes to a given value
Preimage resistance is a security property of cryptographic hash functions. A hash function $H$ is said to be (first) preimage resistant if, given a hash value $x$, it is computationally infeasible to find a string $s$ such that $H(s) = x$.
Stronger security properties often demanded of hash functions include second preimage resistance and collision resistance, both of which imply first preimage resistance.
See also: 2nd-preimage-resistance, collision-resistance