UOWHFs from OWFs: Trading Regularity for Efficiency

Barhum, Kfir; Maurer, Ueli

doi:10.1007/978-3-642-33481-8_13

Cited by 7 publications

(9 citation statements)

References 8 publications

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“…Note that the bound given in [5] does not say anything for the mere construction of a UOWHF (e.g., for a function which compresses one bit), and prior to our work it would have been possible to conjecture that there exists a construction of a UOWHF from a general one-way function that makes only one call to the underlying one-way function. Our bound matches exactly and up to a log-factor the number of calls made by the constructions of [4] and [1], respectively.…”

Section: Our Contributionsupporting

confidence: 53%

A Cookbook for Black-Box Separations and a Recipe for UOWHFs

Barhum

Holenstein

2013

Theory of Cryptography

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Abstract. We present a new framework for proving fully black-box separations and lower bounds. We prove a general theorem that facilitates the proofs of fully black-box lower bounds from a one-way function (OWF).Loosely speaking, our theorem says that in order to prove that a fully black-box construction does not securely construct a cryptographic primitive Q (e.g., a pseudo-random generator or a universal one-way hash function) from a OWF, it is enough to come up with a large enough set of functions F and a parameterized oracle (i.e., an oracle that is defined for every f ∈ {0, 1} n → {0, 1} n ) such that O f breaks the security of the construction when instantiated with f and the oracle satisfies two local properties.Our main application of the theorem is a lower bound of Ω(n/ log(n)) on the number of calls made by any fully black-box construction of a universal one-way hash function (UOWHF) from a general one-way function. The bound holds even when the OWF is regular, in which case it matches to a recent construction of Barhum and Maurer [4].

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Section: Our Contributionsupporting

confidence: 53%

A Cookbook for Black-Box Separations and a Recipe for UOWHFs

Barhum

Holenstein

2013

Theory of Cryptography

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“…Ames et al [1] presented an even more efficient construction of UOWHFs from (unknown) regular one-way functions. Barhum and Maurer [2] gave even a more efficient construction assuming the regularity of the one-way function is known, where Yu et al [32] improved the result of [2] presenting an almost optimal construction (with respect to the known black-box impossibility results) of UOWHFs from known-regular one-way functions.…”

Section: Related Workmentioning

confidence: 99%

“…Thus, B must fail to be correct on some y ∈ L. In fact, there exist infinitely many n's in N and a function δ = δ (n) ∈ (0, 1]. such that B 1 (y, 1 n , δ ; •) is not 2 3 -correct for more than a fraction δ of the inputs y ∈ R L produced by D(1 n , •).…”

Section: Search Heuristics B Amentioning

confidence: 99%

“…Fix m and ε, and let the random variables Y , J, G and R be uniformly chosen from {0, 1} m × [m d + 2] × G m d +2 × {0, 1} . For y ∈ {0, 1} m , let η(y) be the probability that A(y, J, G, 1 n , δ ; •) is not 2 3 -correct. Since E[η(Y )] ≤ δ = ii.…”

Section: A Difficult Problem For the Uniform Distributionmentioning

confidence: 99%

“…Rompel [26] gave a more involved construction to prove that UOWHFs can be constructed from an arbitrary one-way function, thereby resolving the complexity of UOWHFs (as one-way functions are the minimal complexity assumption for complexity-based cryptography, and are easily implied by UOWHFs); this remains the state of the art for arbitrary one-way functions. 2 While complications may be expected for constructions from arbitrary one-way functions (due to their lack of structure), Rompel's analysis also feels quite ad hoc. In contrast, the construction of pseudorandom generators from one-way functions in [15], while also somewhat complex, involves natural abstractions (e. g., pseudoentropy) that allow for modularity and measure for what is being achieved at each stage of the construction.…”

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confidence: 99%

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Haitner¹,

Holenstein²,

Reingold³

et al. 2020

Theory of Comput.

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This paper uses a variant of the notion of inaccessible entropy (Haitner, Reingold, Vadhan and Wee, STOC 2009), to give an alternative construction and proof for the fundamental result, first proved by Rompel (STOC 1990), that Universal One-Way Hash Functions (UOWHFs) can be based on any one-way functions. We observe that a small tweak of any one-way function f is already a weak form of a UOWHF: consider the function F(x, i) that returns the i-bit-long prefix of f (x). If F were a UOWHF then given a random x and i it would be hard to come up with x = x such that F(x, i) = F(x , i). While this may not be the A preliminary version of this paper appeared as "Universal One-Way Hash Functions via Inaccessible Entropy" in EUROCRYPT 2010 [9].

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Simple Constructions from (Almost) Regular One-Way Functions

Mazor

Zhang

2021

Theory of Cryptography

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UOWHFs from OWFs: Trading Regularity for Efficiency

Cited by 7 publications

References 8 publications

A Cookbook for Black-Box Separations and a Recipe for UOWHFs

A Cookbook for Black-Box Separations and a Recipe for UOWHFs

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Simple Constructions from (Almost) Regular One-Way Functions

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