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Questions tagged [universal-hash]

In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property.

Universal hashing guarantees a low number of collisions in expectation, even if the data is chosen by an adversary. Many universal families are known (for hashing integers, vectors, strings), and their evaluation is often very efficient. Universal hashing has numerous uses in computer science, for example in implementations of hash tables, randomized algorithms, and cryptography.

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Universal hash functions with homomorphic XOR property

Let $H = \{h_r : U \rightarrow [m]\}$. What are the currently known most efficient algorithms such that $H$ is a universal family and fulfils the homomorphic XOR operation property $\forall h \in H \forall x,y \in U: h(x \oplus y) = h(x) \oplus…
Martin Kromm
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How does the probabilty for universal hashing work out?

Hey for universal hashing we say the following: Definition: A randomized algorithm $H$ for constructing hash functions $h\colon U \to \{1,\ldots,M\}$ is universal if for all $x \neq y$ in $U$, we have $\Pr_{h\gets H} [h(x) = h(y)] \leq 1/M$ I…
OuttaSpaceTime
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Why does the hashfamily of all functions with $\{h \in H_0 | h:U \rightarrow V\}$ satisfy universal hashing?

I read in our university lecture on hashing that it would be good (even though it is way to space intensive) if we could take the set of all function from $U \rightarrow V$ to satisfy the following universal hashing condition: for all $\forall…
OuttaSpaceTime
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Why do universal hash functions prevent adversarys, but uniform hash functions don't?

Before I state my actual question, let me first five some terminology so we are all on the same page: Let $U=\{k_1,...,k_u\}$ the universe of possible keys, $|U|=u$. We use a hash table $T$ with $m$ cells, counting from $0$ to $m-1$. We use a family…
Prof.Chaos
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PRF and pairwise independent hash function

I'm confused with the concepts of pairwise independent hash function and pseudorandom function. They seem identical to me. A family of hash functions $H=\{ h:U \to [m] \}$ is $k$-independent if for any $k$ distinct keys $(x_1, \dots, x_k) \in U^k$…
A.Solei
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Combining two almost universal hash functions

We say that a set of functions $S$ is $\epsilon$-almost-universal if for any function $f \in S$, it holds that $\Pr[f(m) = f(m')] < \epsilon$ for $m \not = m'$. Assume that we have the following two sets of hash functions: $F = \{f:M \rightarrow…
Digimon Kaiser
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Hash function with good performance on extremely short messages

Are there randomized almost universal hashes that are fast for extremely short messages (usually <10 bytes)? Edit: This is for hash tables, so it only needs to be hard enough to break to make the HashDOS attack not worthwhile. I am specifically…
Demi
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