Multi-Collision Resistant Hash Functions and Their Applications

Berman, Itay; Degwekar, Akshay; Rothblum, Ron D.; Vasudevan, Prashant Nalini

doi:10.1007/978-3-319-78375-8_5

Cited by 28 publications

(8 citation statements)

References 35 publications

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“…Multi-collisions algorithms have also been used in attacks, such as the MDC-2 [KMRT09], HMAC [NSWY13], Even-Mansour [DDKS14], and LED [NWW14]. Multicollision resistance for polynomial k has also recently emerged as a theoretical way to avoid keyed hash functions [BKP18,BDRV18], or as a useful cryptographic primitives, for example, to build statistically hiding commitment schemes with succinct interaction [KNY18].…”

Section: Introductionmentioning

confidence: 99%

On Finding Quantum Multi-collisions

Liu

Zhandry

2019

Advances in Cryptology – EUROCRYPT 2019

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A k-collision for a compressing hash function H is a set of k distinct inputs that all map to the same output. In this work, we show that for any constant k, Θ N 1 2 (1− 1 2 k −1 ) quantum queries are both necessary and sufficient to achieve a k-collision with constant probability. This improves on both the best prior upper bound (Hosoyamada et al., ASIACRYPT 2017) and provides the first non-trivial lower bound, completely resolving the problem.

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Section: Introductionmentioning

confidence: 99%

On Finding Quantum Multi-collisions

Liu

Zhandry

2019

Advances in Cryptology – EUROCRYPT 2019

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“…Using this oracle, Asharov and Segev [3] proves the separation result of CRH from OWP and indistinguishability obfuscators. Berman et al [7] proves the separation result of MCRH from OWP. We follow their work and show a similar result about k-rSRH.…”

Section: Proofmentioning

confidence: 86%

“…In 2005, Haitner et al [21] prove the fully black-box separation of constant-round statistically-hiding commitment schemes from one-way permutations. Furthermore, Berman et al [7] and Komargodski et al [29] independently construct constant-round statisticallyhiding commitment schemes from MCRH in fully black-box manners. This rules out the possibility of constructing an MCRH from one-way permutations in fully black-box manners.…”

Section: Black-box Separationmentioning

confidence: 99%

On subset-resilient hash function families

Yuan

Tibouchi

Abe

2022

Des. Codes Cryptogr.

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In this paper, we analyze the security of subset-resilient hash function families, which is first proposed as a requirement of a hash-based signature scheme called HORS. Let $${\mathcal {H}}$$ H be a family of functions mapping an element to a subset of size at most k. (r, k)-subset resilience guarantees that given a random function H from $${\mathcal {H}}$$ H , it is hard to find an $$(r+1)$$ ( r + 1 ) -tuple $$(x,x_1,\ldots ,x_r)$$ ( x , x 1 , … , x r ) such that (1) H(x) is covered by the union of $$H(x_i)$$ H ( x i ) and (2) x is not equal to any $$x_i$$ x i . Subset resilience and its variants are related to nearly all existing stateless hash-based signature schemes, but the power of this security notion is lacking in research. We present three results on subset resilience. First, we show a generic quantum attack against subset resilience, whose time complexity is smaller than simply implementing Grover’s search. Second, we show that subset-resilient hash function families imply the existence of distributional collision-resistant hash function families. Informally, distributional collision resistance is a relaxation of collision resistance, which guarantees that it is hard to find a uniform collision for a hash function. This result implies a comparison among the power of subset resilience, collision resistance, and distributional collision resistance. Third, we prove the fully black-box separation from one-way permutations.

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“…Constant-round statistically hiding commitment protocols are known to exist based on families of collision resistant hash functions [NY89,DPP93,HM96]. Recently, Berman, Degwekar, Rothblum and Vasudevan [BDRV18] and Komargodski, Naor and Yogev [KNY18] constructed constant-round statistically hiding commitment protocols assuming the existence of multi -collision resistant hash functions.…”

Section: Related Work On Statistically Hiding Commitmentsmentioning

confidence: 99%

“…2 (let alone plain collision resistance). This can be seen as evidence suggesting that dCRH may be weaker than collision resistance, or even multi-collision resistance [KNY17,BDRV18,BKP18,KNY18].…”

Section: Introductionmentioning

confidence: 99%

Distributional Collision Resistance Beyond One-Way Functions

Bitansky

Haitner

Komargodski

et al. 2019

Advances in Cryptology – EUROCRYPT 2019

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Distributional collision resistance is a relaxation of collision resistance that only requires that it is hard to sample a collision (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. The notion lies between one-wayness and collision resistance, but its exact power is still not well-understood. On one hand, distributional collision resistant hash functions cannot be built from one-way functions in a black-box way, which may suggest that they are stronger. On the other hand, so far, they have not yielded any applications beyond one-way functions.Assuming distributional collision resistant hash functions, we construct constant-round statistically hiding commitment scheme. Such commitments are not known based on one-way functions and are impossible to obtain from one-way functions in a black-box way. Our construction relies on the reduction from inaccessible entropy generators to statistically hiding commitments by Haitner et al. (STOC '09). In the converse direction, we show that two-message statistically hiding commitments imply distributional collision resistance, thereby establishing a loose equivalence between the two notions.A corollary of the first result is that constant-round statistically hiding commitments are implied by average-case hardness in the class SZK (which is known to imply distributional collision resistance). This implication seems to be folklore, but to the best of our knowledge has not been proven explicitly. We provide yet another proof of this implication, which is arguably more direct than the one going through distributional collision resistance.

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Multi-Collision Resistant Hash Functions and Their Applications

Cited by 28 publications

References 35 publications

On Finding Quantum Multi-collisions

On Finding Quantum Multi-collisions

On subset-resilient hash function families

Distributional Collision Resistance Beyond One-Way Functions

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