Uniform Hashing in Constant Time and Optimal Space

Pagh, Anna; Pagh, Rasmus

doi:10.1137/060658400

Cited by 71 publications

(132 citation statements)

References 21 publications

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“…The Hash Function Family G. Pagh and Pagh [PP08] and Dietzfelbinger and Woelfel [DW03] (see also Aumuller et al [ADW14]) showed how to construct a family G of hash functions g : U → V so that on any set of k inputs it behaves like a truly random function with high probability (1 − 1/poly(k)). Furthermore, g can be evaluated in constant time (in the RAM model), and its description can be stored using (1 + α)k log |V | + O(k) bits (where here α is an arbitrarily small constant).…”

Section: Computationally Unbounded Adversarymentioning

confidence: 99%

“…Since each element is compared only with two cells, this lets us improve the analysis of the reduction which reduce the size of V to O 1 ε (instead of n ε ). To initialize the hash function g, instead of using a universal hash function we use a very high independence function (which in turn is also constructed based on cuckoo hashing) based on the work of Pagh and Pagh [PP08] and Dietzfelbinger and Woelfel [DW03]. They showed how to construct a family G of hash functions so that on any given set of k inputs it behaves like a truly random function with high probability.…”

Section: Computationally Unbounded Adversariesmentioning

confidence: 99%

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Bloom Filters in Adversarial Environments

Naor

Yogev

2015

Lecture Notes in Computer Science

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Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and/or correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are independent of the internal randomness of the data structure. In this work, we consider data structures in a more robust model, which we call the adversarial model. Roughly speaking, this model allows an adversary to choose inputs and queries adaptively according to previous responses. Specifically, we consider a data structure known as "Bloom filter" and prove a tight connection between Bloom filters in this model and cryptography.A Bloom filter represents a set S of elements approximately, by using fewer bits than a precise representation. The price for succinctness is allowing some errors: for any x ∈ S it should always answer 'Yes', and for any x / ∈ S it should answer 'Yes' only with small probability. In the adversarial model, we consider both efficient adversaries (that run in polynomial time) and computationally unbounded adversaries that are only bounded in the amount of queries they can make. For computationally bounded adversaries, we show that non-trivial (memory-wise) Bloom filters exist if and only if one-way functions exist. For unbounded adversaries we show that there exists a Bloom filter for sets of size n and error ε, that is secure against t queries and uses only O(n log 1 ε + t) bits of memory. In comparison, n log 1 ε is the best possible under a non-adaptive adversary.

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Section: Computationally Unbounded Adversarymentioning

confidence: 99%

Section: Computationally Unbounded Adversariesmentioning

confidence: 99%

Bloom Filters in Adversarial Environments

Naor

Yogev

2015

Lecture Notes in Computer Science

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Section: Cuckoo Hashing and Many-wise Independent Hash Functionmentioning

confidence: 99%

“…Pagh and Pagh [42] showed that when the families H and G are of "high enough" independence, that is, roughly (c · log |S|)-wise independent, then the family PP(H, G, Π) is O(|S| −c )-indistinguishable from random by a |S|-query, non-adaptive distinguisher, where Π is the set of all functions from S to R. Note that the security of the resulting family goes well beyond the birthday attack barrier: it is indistinguishable from random by an attacker making |S| |S| queries. Aumüller et al [4] (building on the work of Dietzfelbinger and Woelfel [15]) strengthen the result of [42] by using more sophisticated hash functions H and G (rather than the O(log |S|)-wise independent that [42] used). Specifically, for a given s ≥ 0, Aumüller et al [4] constructed a function family ADW s (H, G, Π) that is O(|S| −(s+1) )-indistinguishable from random by a |S|-query, non-adaptive distinguisher, where Π is the set of all functions from S to R. 2 The idea to use more sophisticated hash functions, in the sense that they require less combinatorial work, already appeared in previous works, e.g., the work of Arbitman et al [2, §5.4].…”

Section: Cuckoo Hashing and Many-wise Independent Hash Functionmentioning

confidence: 99%

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Hardness Preserving Reductions via Cuckoo Hashing

Berman

Haitner

Komargodski

et al. 2013

Theory of Cryptography

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The focus of this work is hardness-preserving transformations of somewhat limited pseudorandom functions families (PRFs) into ones with more versatile characteristics. Consider the problem of domain extension of pseudorandom functions: given a PRF that takes as input elements of some domain U, we would like to come up with a PRF over a larger domain. Can we do it with little work and without significantly impacting the security of the system? One approach is to first hash the larger domain into the smaller one and then apply the original PRF. Such a reduction, however, is vulnerable to a "birthday attack": after |U| queries to the resulting PRF, a collision (i.e., two distinct inputs having the same hash value) is very likely to occur. As a consequence, the resulting PRF is insecure against an attacker making this number of queries.In this work we show how to go beyond the aforementioned birthday attack barrier by replacing the above simple hashing approach with a variant of cuckoo hashing, a hashing paradigm that resolves collisions in a table by using two hash functions and two tables, cleverly assigning each element to one of the two tables. We use this approach to obtain: (i) a domain extension method that requires just two calls to the original PRF, can withstand as many queries as the original domain size, and has a distinguishing probability that is exponentially small in the amount of non-cryptographic work; and (ii) a security-preserving reduction from non-adaptive to adaptive PRFs.

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PSI from PaXoS: Fast, Malicious Private Set Intersection

Pinkas

Rosulek

Trieu

et al. 2020

Advances in Cryptology – EUROCRYPT 2020

104

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We present a 2-party private set intersection (PSI) protocol which provides security against malicious participants, yet is almost as fast as the fastest known semi-honest PSI protocol of Kolesnikov et al. (CCS 2016). Our protocol is based on a new approach for two-party PSI, which can be instantiated to provide security against either malicious or semi-honest adversaries. The protocol is unique in that the only difference between the semi-honest and malicious versions is an instantiation with different parameters for a linear error-correction code. It is also the first PSI protocol which is concretely efficient while having linear communication and security against malicious adversaries, while running in the OT-hybrid model (assuming a non-programmable random oracle). State of the art semi-honest PSI protocols take advantage of cuckoo hashing, but it has proven a challenge to use cuckoo hashing for malicious security. Our protocol is the first to use cuckoo hashing for malicious-secure PSI. We do so via a new data structure, called a probe-and-XOR of strings ( ), which may be of independent interest. This abstraction captures important properties of previous data structures, most notably garbled Bloom filters. While an encoding by a garbled Bloom filter is larger by a factor of than the original data, we describe a significantly improved based on cuckoo hashing that achieves constant rate while being no worse in other relevant efficiency measures.

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Uniform Hashing in Constant Time and Optimal Space

Cited by 71 publications

References 21 publications

Bloom Filters in Adversarial Environments

Bloom Filters in Adversarial Environments

Hardness Preserving Reductions via Cuckoo Hashing

PSI from PaXoS: Fast, Malicious Private Set Intersection

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