Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2211.16993

Post-Quantum κκκ-to-1 Trapdoor Claw-free Functions from Extrapolated Dihedral Cosets

Xingyu Yan, Licheng Wang, Lize Gu, Ziyi Li, Jingwen Suo

Published Nov 30, 2022• 0 citations
arXivHTMLPDF

Abstract

\emph{Noisy trapdoor claw-free function} (NTCF) as a powerful post-quantum cryptographic tool can efficiently constrain actions of untrusted quantum devices. However, the original NTCF is essentially \emph{2-to-1} one-way function (NTCF$^1_2$). In this work, we attempt to further extend the NTCF$^1_2$ to achieve \emph{many-to-one} trapdoor claw-free functions with polynomial bounded preimage size. Specifically, we focus on a significant extrapolation of NTCF$^1_2$ by drawing on extrapolated dihedral cosets, thereby giving a model of NTCF$^1_κ$ where $κ$ is a polynomial integer. Then, we present an efficient construction of NTCF$^1_κ$ assuming \emph{quantum hardness of the learning with errors (LWE)} problem. We point out that NTCF can be used to bridge the LWE and the dihedral coset problem (DCP). By leveraging NTCF$^1_2$ (resp. NTCF$^1_κ$), our work reveals a new quantum reduction path from the LWE problem to the DCP (resp. extrapolated DCP). Finally, we demonstrate the NTCF$^1_κ$ can naturally be reduced to the NTCF$^1_2$, thereby achieving the same application for proving the quantumness.

DOI
10.48550/arxiv.2211.16993

Related papers

A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device

Zvika Brakerski, Paul F. Christiano, Urmila Mahadev +2 more

We consider a new model for the testing of untrusted quantum devices, consisting of a single polynomial time bounded quantum device interacting with a classical polynomial time verifier. In this model, we propose solutions to two tasks—a protocol for efficient classical verification that the untrusted device is “truly quantum” and a protocol for producing certifiable randomness from a single untrusted quantum device. Our solution relies on the existence of a new cryptographic primitive for constraining the power of an untrusted quantum device: post-quantum secure trapdoor claw-free functions that must satisfy an adaptive hardcore bit property. We show how to construct this primitive based on the hardness of the learning with errors (LWE) problem.

arXiv:1804.00640•Journal of the ACM•Aug 12, 2021•60 citations

Post-quantum κ\kappa κ-to-1 trapdoor claw-free functions from extrapolated dihedral cosets

Xingyu Yan, Licheng Wang, Lize Gu +2 more

Quantum Information Processing•May 13, 2024•0 citations

Computationally Secure Semi‐Quantum All‐Or‐Nothing Oblivious Transfer from Dihedral Coset States

Xingyu Yan, Licheng Wang, Lize Gu

Abstract The quest for perfect quantum oblivious transfer (QOT) with information‐theoretic security remains a challenge, necessitating the exploration of computationally secure QOT as a viable alternative. Unlike the unconditionally secure quantum key distribution (QKD), the computationally secure QOT relies on specific quantum‐safe computational hardness assumptions, such as the post‐quantum hardness of learning with errors (LWE) problem and quantum‐hard one‐way functions. This raises an intriguing question: Are there additional efficient quantum hardness assumptions that are suitable for QOT? In this work, leveraging the dihedral coset state derived from the dihedral coset problem (DCP), a basic variant of OT, known as the all‐or‐nothing OT, is studied in the semi‐quantum setting. Specifically, the DCP originates from the dihedral hidden subgroup problem (DHSP), conjectured to be challenging for any quantum polynomial‐time algorithms. First, a computationally secure quantum protocol is presented for all‐or‐nothing OT, which is then simplified into a semi‐quantum OT protocol with minimal quantumness, where the interaction needs merely classical communication. To efficiently instantiate the dihedral coset state, a powerful cryptographic tool called the LWE‐based noisy trapdoor claw‐free functions (NTCFs) is used. The construction requires only a three‐message interaction and ensures perfect statistical privacy for the receiver and computational privacy for the sender.

Advanced Quantum Technologies•Apr 14, 2024•5 citations

Better Quantum Seal Schemes based on Trapdoor Claw-Free Functions

Xiaogang Cheng, Ren Guo

Seal in classical information is simply impossible. Since classical information can be easily copied any number of times. Based on quantum information, esp. quantum unclonable theorem, quantum seal maybe constructed perfectly. But it is shown that perfect quantum seal is impossible, and the success probability is bounded. In this paper, we show how to exceed the optimal bound by using the TCF (Trapdoor Claw Free) functions, which can be constructed based on LWE assumption. Hence it is post-quantum secure.

arXiv:2308.12310•Aug 23, 2023•0 citations

On the Construction of Trapdoor Claw-Free Functions with Certifiable Key

Charles Lim, Yao Ma

Trapdoor claw-free functions (TCFs) underpin much of classical-quantum cryptographic interaction, yet every TCF-based protocol states its guarantees relative to an honestly generated key. We give a family-agnostic abstraction of key certification for (noisy) TCF constructions, built on two notions: a certifiable key relation, an NP relation capturing a family's honest keys with witnesses recoverable from the trapdoor; and certified key generation, which emits with each key a certificate of membership satisfying completeness, certificate soundness with extractability, and key privacy. We instantiate certifiable key relations for different constructions, each met generically by a zero-knowledge argument of knowledge for the relation. As our main application, a generic compiler turns any TCF-based proof of quantumness into a zero-knowledge one, with each security property following from its counterpart in the certification scheme. Finally, we delimit the primitive's reach: for protocols resting on injective invariance, an accepting certificate is itself a family distinguisher, leaking exactly the bit such protocols must hide.

cs.CRCross-listedarXiv:2609.25819•Sep 23, 2026•0 citations

A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device

Zvika Brakerski, Paul F. Christiano, Urmila Mahadev +2 more

We give a protocol for producing certifiable randomness from a single untrusted quantum device that is polynomial-time bounded. The randomness is certified to be statistically close to uniform from the point of view of any computationally unbounded quantum adversary, that may share entanglement with the quantum device. The protocol relies on the existence of post-quantum secure trapdoor claw-free functions, and introduces a new primitive for constraining the power of an untrusted quantum device. We then show how to construct this primitive based on the hardness of the learning with errors (LWE) problem. The randomness protocol can also be used as the basis for an efficiently verifiable "quantum supremacy" proposal, thus answering an outstanding challenge in the field.

Annual Symposium on Foundations of Computer Science•Oct 1, 2018•85 citations
\emph{Noisy trapdoor claw-free function} (NTCF) as a powerful post-quantum cryptographic tool can efficiently constrain actions of untrusted quantum devices. However, the original NTCF is essentially \emph{2-to-1} one-way function (NTCF21^1_221​). In this work, we attempt to further extend the NTCF21^1_221​ to achieve \emph{many-to-one} trapdoor claw-free functions with polynomial bounded preimage size. Specifically, we focus on a significant extrapolation of NTCF21^1_221​ by drawing on extrapolated dihedral cosets, thereby giving a model of NTCFκ1^1_κκ1​ where κκκ is a polynomial integer. Then, we present an efficient construction of NTCFκ1^1_κκ1​ assuming \emph{quantum hardness of the learning with errors (LWE)} problem. We point out that NTCF can be used to bridge the LWE and the dihedral coset problem (DCP). By leveraging NTCF21^1_221​ (resp. NTCFκ1^1_κκ1​), our work reveals a new quantum reduction path from the LWE problem to the DCP (resp. extrapolated DCP). Finally, we demonstrate the NTCFκ1^1_κκ1​ can naturally be reduced to the NTCF21^1_221​, thereby achieving the same application for proving the quantumness.
We consider a new model for the testing of untrusted quantum devices, consisting of a single polynomial time bounded quantum device interacting with a classical polynomial time verifier. In this model, we propose solutions to two tasks—a protocol for efficient classical verification that the untrusted device is “truly quantum” and a protocol for producing certifiable randomness from a single untrusted quantum device. Our solution relies on the existence of a new cryptographic primitive for constraining the power of an untrusted quantum device: post-quantum secure trapdoor claw-free functions that must satisfy an adaptive hardcore bit property. We show how to construct this primitive based on the hardness of the learning with errors (LWE) problem.
Abstract The quest for perfect quantum oblivious transfer (QOT) with information‐theoretic security remains a challenge, necessitating the exploration of computationally secure QOT as a viable alternative. Unlike the unconditionally secure quantum key distribution (QKD), the computationally secure QOT relies on specific quantum‐safe computational hardness assumptions, such as the post‐quantum hardness of learning with errors (LWE) problem and quantum‐hard one‐way functions. This raises an intriguing question: Are there additional efficient quantum hardness assumptions that are suitable for QOT? In this work, leveraging the dihedral coset state derived from the dihedral coset problem (DCP), a basic variant of OT, known as the all‐or‐nothing OT, is studied in the semi‐quantum setting. Specifically, the DCP originates from the dihedral hidden subgroup problem (DHSP), conjectured to be challenging for any quantum polynomial‐time algorithms. First, a computationally secure quantum protocol is presented for all‐or‐nothing OT, which is then simplified into a semi‐quantum OT protocol with minimal quantumness, where the interaction needs merely classical communication. To efficiently instantiate the dihedral coset state, a powerful cryptographic tool called the LWE‐based noisy trapdoor claw‐free functions (NTCFs) is used. The construction requires only a three‐message interaction and ensures perfect statistical privacy for the receiver and computational privacy for the sender.
Seal in classical information is simply impossible. Since classical information can be easily copied any number of times. Based on quantum information, esp. quantum unclonable theorem, quantum seal maybe constructed perfectly. But it is shown that perfect quantum seal is impossible, and the success probability is bounded. In this paper, we show how to exceed the optimal bound by using the TCF (Trapdoor Claw Free) functions, which can be constructed based on LWE assumption. Hence it is post-quantum secure.
Trapdoor claw-free functions (TCFs) underpin much of classical-quantum cryptographic interaction, yet every TCF-based protocol states its guarantees relative to an honestly generated key. We give a family-agnostic abstraction of key certification for (noisy) TCF constructions, built on two notions: a certifiable key relation, an NP relation capturing a family's honest keys with witnesses recoverable from the trapdoor; and certified key generation, which emits with each key a certificate of membership satisfying completeness, certificate soundness with extractability, and key privacy. We instantiate certifiable key relations for different constructions, each met generically by a zero-knowledge argument of knowledge for the relation. As our main application, a generic compiler turns any TCF-based proof of quantumness into a zero-knowledge one, with each security property following from its counterpart in the certification scheme. Finally, we delimit the primitive's reach: for protocols resting on injective invariance, an accepting certificate is itself a family distinguisher, leaking exactly the bit such protocols must hide.
We give a protocol for producing certifiable randomness from a single untrusted quantum device that is polynomial-time bounded. The randomness is certified to be statistically close to uniform from the point of view of any computationally unbounded quantum adversary, that may share entanglement with the quantum device. The protocol relies on the existence of post-quantum secure trapdoor claw-free functions, and introduces a new primitive for constraining the power of an untrusted quantum device. We then show how to construct this primitive based on the hardness of the learning with errors (LWE) problem. The randomness protocol can also be used as the basis for an efficiently verifiable "quantum supremacy" proposal, thus answering an outstanding challenge in the field.