Explicit and Efficient Hash Families Suffice for Cuckoo Hashing with a Stash

  title={Explicit and Efficient Hash Families Suffice for Cuckoo Hashing with a Stash},
  author={Martin Aum{\"u}ller and Martin Dietzfelbinger and Philipp Woelfel},
It is shown that for cuckoo hashing with a stash as proposed by Kirsch et al. (Proc. 16th European Symposium on Algorithms (ESA), pp. 611–622, Springer, Berlin, 2008) families of very simple hash functions can be used, maintaining the favorable performance guarantees: with constant stash size s the probability of a rehash is O(1/ns+1), the lookup time and the deletion time are O(s) in the worst case, and the amortized expected insertion time is O(s) as well. Instead of the full randomness… 

An Intimate Analysis of Cuckoo Hashing with a Stash

  • D. Noble
  • Computer Science
    IACR Cryptol. ePrint Arch.
  • 2021
A tighter analysis is presented which shows failure probability negligible in N for all n = ω(log(N)) (which is asymptotically optimal) and presents explicit constants for the failure probability upper bound.

Alibi: A Flaw in Cuckoo-Hashing based Hierarchical ORAM Schemes and a Solution

This work identifies a subtle flaw in the protocol of Goodrich et al. (SODA ’12) that uses cuckoo hashing with a stash in the hierarchical OrAM solution, and gives a concrete distinguishing attack against this type of hierarchical ORAM that usescuckoo hacking with a combined stash.

Explicit, Closed-form, General bounds for Cuckoo Hashing with a Stash

  • D. Noble
  • Computer Science, Mathematics
  • 2022
This paper presents the first explicit, closed-form bounds for the failure probability of cuckoo hashing with a stash for general stash sizes, and applies to super-constant s where s is any constant stash size.

Insertion Time of Random Walk Cuckoo Hashing below the Peeling Threshold

This paper shows that random walk insertions into cuckoo hash tables take O (1) expected amortised time when any number k ≥ 3 of hash functions is used and the load factor is below the corresponding peeling threshold.

Cuckoo Hashing in Cryptography: Optimal Parameters, Robustness and Applications

  • Kevin Yeo
  • Computer Science, Mathematics
    IACR Cryptol. ePrint Arch.
  • 2022
This work presents a more efficient cuckoo hashing construction using more hash functions, and presents the most efficient explicit batch code and blackbox reduction from single-query PIR to batch PIR.

Multi-copy Cuckoo Hashing

An efficient Cuckoo hashing scheme called Multi-copy Cuckoos or McCuckoo is proposed, which can foresee which way to successfully kick items by using multiple copies during a collision, and identify impossible buckets and skip them during a lookup.

Twisted Tabulation Hashing

We introduce a new tabulation-based hashing scheme called "twisted tabulation". It is essentially as simple and fast as simple tabulation, but has some powerful distributional properties illustrating

A Fully-Constructive Discrete-Logarithm Preprocessing Algorithm with an Optimal Time-Space Tradeoff

A fully constructive discrete-logarithm preprocessing algorithm with an asymptotically optimal space-time tradeoff is presented, and an algorithm is obtained that settles the corresponding tradeoff for the computational Diffie-Hellman problem.

Pseudorandom Graphs in Data Structures

We prove that the hash functions required for several data structure applications could be instantiated using the hash functions of Celis et al. (SIAM J. Comput., 2013). These functions

Tight Tradeoffs in Searchable Symmetric Encryption

This work introduces the “pad-and-split” framework, and establishes tight bounds on the tradeoff between the space overhead, locality and read efficiency of SSE schemes within two general frameworks that capture the memory access pattern underlying all existing schemes.



Explicit and Efficient Hash Families Suffice for Cuckoo Hashing with a Stash

It is shown that for cuckoo hashing with a stash as proposed by Kirsch et al. families of very simple hash functions can be used, maintaining the favorable performance guarantees, and can be generalized to situations where the stash size is non-constant.

On risks of using cuckoo hashing with simple universal hash classes

It is proved that the failure probability is high when cuckoo hashing is run with the multiplicative class or with the very common class of linear hash functions over a prime field, even if space 4n is provided.

A further analysis of Cuckoo Hashing with a Stash and Random Graphs of Excess r

It is shown that the same bounds on the failure probability hold even without this search process and thus, the performance increases, and some explicit asymptotic approximations concerning the number of usual resp.

Why simple hash functions work: exploiting the entropy in a data stream

It is demonstrated that the strong performance of universal hash functions in practice can arise naturally from a combination of the randomness of the hash function and the data.

Space Efficient Hash Tables with Worst Case Constant Access Time

This is the first dictionary that has worst case constant access time and expected constant update time, works with (1 + ε)n space, and supports satellite information.

Tabulation Based 5-Universal Hashing and Linear Probing

If the pre-computed tables are made 5-universal, then the hash value becomes 5- universal without any other change to the computation, which leads to even bigger gains since the direct methods for 5-Universal hashing use degree 4 polynomials.

Almost random graphs with simple hash functions

The main new technique is the combined analysis of the graph structure and the inner structure of the hash functions, as well as a new way of looking at the cycle structure of random (multi)graphs.

Applications of a Splitting Trick

Three new applications of a simple method for circumventing the "full randomness assumption" when building a hashing-based data structure for a set S of keys, introduced in the context of cuckoo hashing and its variants are studied.

Cuckoo Hashing

A simple dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al, and is competitive with the best known dictionaries having an average case (but no nontrivial worst case) guarantee on lookup time.

Uniform Hashing in Constant Time and Optimal Space

This paper presents an almost ideal solution to this problem: a hash function h: U: Uarrow V that, on any set of $n$ inputs, behaves like a truly random function with high probability, can be evaluated in constant time on a RAM and can be stored in $(1+\epsilon)n\log |V| + O(n+\log \log |U|)$ bits.