A second preimage resistance strength, with the same expectations, refers to a similar problem of finding a second message that matches the given hash value when one message is already known.If an attacker can obtain the hashes of a set of passwords, they can test each hash value against lists of common passwords and all possible combinations of short passwords and typically recover a large fraction of the passwords themselves. A common example is the use of a standard fast hash function to obscure user passwords in storage. ![]() the probability of a particular n n -bit output result ( hash value) for a random input string ("message") is 2 − n 2^, or if it can be ordered by likelihood, then the hash value can serve as an oracle, allowing efficient search of the limited or ordered input space. ![]() A cryptographic hash function ( CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of n n bits) that has special properties desirable for a cryptographic application:
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