Finding Collisions in a Quantum World: Quantum Black-Box Separation of Collision-Resistance and One-Wayness

Hosoyamada, Akinori; Yamakawa, Takashi

doi:10.1007/978-3-030-64837-4_1

Cited by 14 publications

(10 citation statements)

References 32 publications

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“…In particular, as mentioned several times, the present work is a generalization of a result by Gertner et al [GMM07]. More recently, Hosoyamada et al [HY20] defined the notion of quantum black-box reduction. In addition, they showed that there is no quantum black-box reduction from collision-resistant hash functions to one-way permutations [HY20].…”

Section: Related Worksupporting

confidence: 52%

“…More recently, Hosoyamada et al [HY20] defined the notion of quantum black-box reduction. In addition, they showed that there is no quantum black-box reduction from collision-resistant hash functions to one-way permutations [HY20]. Following this work, Cao et al [CX21] proved that one-way permutations cannot be obtained from different flavours of one-way functions in a quantum black-box way.…”

Section: Related Workmentioning

confidence: 99%

“…Following similar works (e.g. [HY20]), we consider the quantum circuits model of computation, where a quantum algorithm is a family of quantum circuits. In addition, as our quantum adversaries (algorithms) have access to oracles, we must define oracle-aided quantum algorithms.…”

Section: Quantum Algorithmsmentioning

confidence: 99%

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Impossibility of Post-Quantum Shielding Black-Box Constructions of CCA from CPA

Huguenin-Dumittan,

Vaudenay

2024

IACR CiC

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Proving whether it is possible to build IND-CCA public-key encryption (PKE) from IND-CPA PKE in a black-box manner is a major open problem in theoretical cryptography. In a significant breakthrough, Gertner, Malkin and Myers showed in 2007 that shielding black-box reductions from IND-CCA to IND-CPA do not exist in the standard model. Shielding means that the decryption algorithm of the IND-CCA scheme does not call the encryption algorithm of the underlying IND-CPA scheme. In other words, it implies that every tentative construction of IND-CCA from IND-CPA must have a re-encryption step when decrypting. This result was only proven with respect to classical algorithms. In this work we show that it stands in a post-quantum setting. That is, we prove that there is no post-quantum shielding black-box construction of IND-CCA PKE from IND-CPA PKE. In the type of reductions we consider, i.e. post-quantum ones, the constructions are still classical in the sense that the schemes must be computable on classical computers, but the adversaries and the reduction algorithm can be quantum. This suggests that considering quantum notions, which are stronger than their classical counterparts, and allowing for quantum reductions does not make building IND-CCA public-key encryption easier.

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Section: Related Worksupporting

confidence: 52%

Section: Related Workmentioning

confidence: 99%

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Impossibility of Post-Quantum Shielding Black-Box Constructions of CCA from CPA

Huguenin-Dumittan,

Vaudenay

2024

IACR CiC

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“…A quantumly-secure implementation of OWFs and collision-resistant hash functions exists relative to a random oracle [BBBV97,Zha15]. [HY20] implicitly proves that quantumly-secure implementation of trapdoor-permutations exist relative to a classical oracle. We believe that we can prove similar statements for most cryptographic primitives by appropriately defining oracles.…”

Section: Definition 711 (Secure Implementation Relative To Oracles [R...mentioning

confidence: 92%

Quantum Advantage from One-Way Functions

Morimae¹,

Yamakawa²

2023

Preprint

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Showing quantum advantage based on weaker and standard classical complexity assumptions is one of the most important goals in quantum information science. In this paper, we demonstrate quantum advantage with several basic assumptions, specifically based on only the existence of classically-secure one-way functions. We introduce inefficient-verifier proofs of quantumness (IV-PoQ), and construct it from statistically-hiding and computationallybinding classical bit commitments. IV-PoQ is an interactive protocol between a verifier and a quantum polynomialtime prover consisting of two phases. In the first phase, the verifier is classical probabilistic polynomial-time, and it interacts with the quantum polynomial-time prover over a classical channel. In the second phase, the verifier becomes inefficient, and makes its decision based on the transcript of the first phase. If the quantum prover is honest, the inefficient verifier accepts with high probability, but any classical probabilistic polynomial-time malicious prover only has a small probability of being accepted by the inefficient verifier. In our construction, the inefficient verifier can be a classical deterministic polynomial-time algorithm that queries an NP oracle. Our construction demonstrates the following results based on the known constructions of statistically-hiding and computationally-binding commitments from one-way functions or distributional collision-resistant hash functions:• If one-way functions exist, then IV-PoQ exist.• If distributional collision-resistant hash functions exist (which exist if hard-on-average problems in SZK exist), then constant-round IV-PoQ exist.We also demonstrate quantum advantage based on worst-case-hard assumptions. We define auxiliary-input IV-PoQ (AI-IV-PoQ) that only require that for any malicious prover, there exist infinitely many auxiliary inputs under which the prover cannot cheat. We construct AI-IV-PoQ from an auxiliary-input version of commitments in a similar way, showing that• If auxiliary-input one-way functions exist (which exist if CZK ⊆ BPP), then AI-IV-PoQ exist.• If auxiliary-input collision-resistant hash functions exist (which is equivalent to PWPP FBPP) or SZK BPP, then constant-round AI-IV-PoQ exist.Finally, we also show that some variants of PoQ can be constructed from quantum-evaluation one-way functions (QE-OWFs), which are similar to classically-secure classical one-way functions except that the evaluation algorithm is not classical but quantum. QE-OWFs appear to be weaker than classically-secure classical one-way functions.

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“…So far, most of the existing black-box separations in quantum cryptography have focused on extending black-box separations for classical cryptographic primitives to the quantum setting. Hosoyamada and Yamakawa [HY20] extend the black-box separation between collision-resistant hash functions and one-way functions [Sim98] to the quantum setting. Austrin, Chung, Chung, Fu, Lin and Mahmoody [ACC+22] showed a black-box separation between key agreement and one-way functions in the setting when the honest parties can perform quantum computation but only have access to classical communication.…”

Section: Related Workmentioning

confidence: 99%

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions

Ananth¹,

Hu²,

Yuen³

2023

Preprint

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Public-key quantum money is a cryptographic proposal for using highly entangled quantum states as currency that is publicly verifiable yet resistant to counterfeiting due to the laws of physics. Despite significant interest, constructing provably-secure public-key quantum money schemes based on standard cryptographic assumptions has remained an elusive goal. Even proposing plausibly-secure candidate schemes has been a challenge.These difficulties call for a deeper and systematic study of the structure of public-key quantum money schemes and the assumptions they can be based on. Motivated by this, we present the first black-box separation of quantum money and cryptographic primitives. Specifically, we show that collision-resistant hash functions cannot be used as a black-box to construct publickey quantum money schemes where the banknote verification makes classical queries to the hash function. Our result involves a novel combination of state synthesis techniques from quantum complexity theory and simulation techniques, including Zhandry's compressed oracle technique.

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Finding Collisions in a Quantum World: Quantum Black-Box Separation of Collision-Resistance and One-Wayness

Cited by 14 publications

References 32 publications

Impossibility of Post-Quantum Shielding Black-Box Constructions of CCA from CPA

Impossibility of Post-Quantum Shielding Black-Box Constructions of CCA from CPA

Quantum Advantage from One-Way Functions

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions

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