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A hash function uniform on the interval [0, n − 1] is n P(key) / 2 b. We can replace the division by a (possibly faster) right bit shift: n P(key) >> b. If keys are being hashed repeatedly, and the hash function is costly, then computing time can be saved by precomputing the hash codes and storing them with the keys.
Typically, a unique salt is randomly generated for each password. The salt and the password (or its version after key stretching) are concatenated and fed to a cryptographic hash function, and the output hash value is then stored with the salt in a database. The salt does not need to be encrypted, because knowing the salt would not help the ...
A cryptographic hash function must be able to withstand all known types of cryptanalytic attack. In theoretical cryptography, the security level of a cryptographic hash function has been defined using the following properties: Pre-image resistance Given a hash value h, it should be difficult to find any message m such that h = hash(m).
A hash table uses a hash function to compute an index, also called a hash code, into an array of buckets or slots, from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. A map implemented by a hash table is called a hash map.
File verification is the process of using an algorithm for verifying the integrity of a computer file, usually by checksum.This can be done by comparing two files bit-by-bit, but requires two copies of the same file, and may miss systematic corruptions which might occur to both files.
Hash-based signature schemes use one-time signature schemes as their building block. A given one-time signing key can only be used to sign a single message securely. Indeed, signatures reveal part of the signing key. The security of (hash-based) one-time signature schemes relies exclusively on the security of an underlying hash function.
This is exactly the probability of collision we would expect if the hash function assigned truly random hash codes to every key. Sometimes, the definition is relaxed by a constant factor, only requiring collision probability O ( 1 / m ) {\displaystyle O(1/m)} rather than ≤ 1 / m {\displaystyle \leq 1/m} .
By definition, an ideal hash function is such that the fastest way to compute a first or second preimage is through a brute-force attack. For an n-bit hash, this attack has a time complexity 2 n, which is considered too high for a typical output size of n = 128 bits. If such complexity is the best that can be achieved by an adversary, then the ...