arXiv subjects

Kun Tian

Publications and source records attributed to Kun Tian.

At least 19 recordsLinked to original sources

arXiv2026

Verifiable and Collusion-Resistant Multi-Party Quantum Private Set Operations

Threshold private set intersection (TPSI) allows parties to reveal their intersection only when its cardinality reaches a prescribed threshold. Existing quantum TPSI protocols typically rely on a third party (TP) to interpret the final results, which deviates from the cardinality-testing paradigm of TPSI. In this paper, we propose a quantum multiparty TPSI protocol with explicit cardinality testing. Our protocol develops a rotation-based quantum construction in which single-photon sequences are sequentially processed through participant-side data rotations, TP--participant masking rotations, and correlated aggregate rotations. This design produces hidden-label measurement vectors: TP can complete the final measurement, but cannot interpret the semantic meaning of the outcomes. Based on these hidden measurements, we further realize the threshold decision through an oblivious linear evaluation (OLE)-based inner product procedure and a lightweight garbled circuit, revealing only $\mathbf 1[|\bigcap_i X_i|\ge \tau]$ before conditional intersection reconstruction. We prove the correctness and security of the proposed protocol, and further validate its feasibility through quantum-circuit simulations implemented on the IBM \textsf{Qiskit} platform.

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arXiv2026

Quantum Multi-Party Threshold Private Set Intersection with Explicit Cardinality Testing

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arXiv2026

Efficient Quantum Fully Homomorphic Encryption

Quantum fully homomorphic encryption (QFHE) enables arbitrary quantum computations on encrypted data, but prior constructions require prohibitive quantum resources--specifically, O(lambda^2) EPR pairs per T-gate evaluation using the Barrington-based approach (DSS16). This paper introduces a unified framework achieving exponential improvement over the generic Barrington-based approach in program length. The central innovation is a novel modular arithmetic program (MA-Program) tailored to learning with errors (LWE) decryption. We show that LWE decryption computes the inner product mod q, a modular inner product that is NOT a symmetric function. Thus, prior symmetric-function optimizations (Sinha's O(n)-state branching programs) do not apply. Our MA-Program tracks partial sums modulus q with state space Z_q requiring O(log q) bits, yielding programs of state count O(lambda) with binary encoding O(log lambda) and length O(lambda log lambda). This reduces the quantum gadget size from O(lambda^2) to O(lambda log^2 lambda) EPR pairs. To achieve a fully classical client, we transfer all quantum resources (EPR preparation, Bell measurements, adaptive error correction) to the server via the MA-Program gadget framework. Clients only perform classical LWE key generation, Pauli key encryption under classical FHE, and no quantum operations; a layered key structure further eliminates circular security assumptions. For parallel computation, we adopt the MBQC framework with flow functions, supporting up to O(log lambda) parallel measurements per layer. This separates offline resource preparation from online adaptive measurement, enabling parallel processing while maintaining deterministic evaluation.

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arXiv2025

StreamForest: Efficient Online Video Understanding with Persistent Event Memory

Multimodal Large Language Models (MLLMs) have recently achieved remarkable progress in video understanding. However, their effectiveness in real-time streaming scenarios remains limited due to storage constraints of historical visual features and insufficient real-time spatiotemporal reasoning. To address these challenges, we propose StreamForest, a novel architecture specifically designed for streaming video understanding. Central to StreamForest is the Persistent Event Memory Forest, a memory mechanism that adaptively organizes video frames into multiple event-level tree structures. This process is guided by penalty functions based on temporal distance, content similarity, and merge frequency, enabling efficient long-term memory retention under limited computational resources. To enhance real-time perception, we introduce a Fine-grained Spatiotemporal Window, which captures detailed short-term visual cues to improve current scene perception. Additionally, we present OnlineIT, an instruction-tuning dataset tailored for streaming video tasks. OnlineIT significantly boosts MLLM performance in both real-time perception and future prediction. To evaluate generalization in practical applications, we introduce ODV-Bench, a new benchmark focused on real-time streaming video understanding in autonomous driving scenarios. Experimental results demonstrate that StreamForest achieves the state-of-the-art performance, with accuracies of 77.3% on StreamingBench, 60.5% on OVBench, and 55.6% on OVO-Bench. In particular, even under extreme visual token compression (limited to 1024 tokens), the model retains 96.8% of its average accuracy in eight benchmarks relative to the default setting. These results underscore the robustness, efficiency, and generalizability of StreamForest for streaming video understanding.

cs.CV↗

arXiv2025

Linearly Homomorphic Ring Signature Scheme over Lattices

Construct the first provably secure linear homomorphic ring signature scheme. Ring signatures allow a signer to anonymously sign a message on behalf of a user group (ring) and are widely applied in areas such as identity protection, electronic voting, and privacy enhancement in blockchain. Homomorphic signatures, on the other hand, support verifiable computations on signed data. The integration of anonymity and computability in homomorphic ring signatures holds the potential to create new application scenarios for privacy-preserving distributed systems. It is worth noting that Choi and Kim first introduced the concept of linear homomorphic ring signatures in 2017 and proposed a specific scheme. However, their scheme lacks a complete security proof, leaving its security theoretically unconfirmed. To address this research gap, this paper presents the first provably secure lattice-based linear homomorphic ring signature scheme, designed for scenarios where the ring size is O(log n). This scheme not only combines the anonymity of ring signatures with the malleability of homomorphic signatures but also achieves resistance against quantum attacks.

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arXiv2025

Authenticated Private Set Intersection: A Merkle Tree-Based Approach for Enhancing Data Integrity

Private Set Intersection (PSI) enables secure computation of set intersections while preserving participant privacy, standard PSI existing protocols remain vulnerable to data integrity attacks allowing malicious participants to extract additional intersection information or mislead other parties. In this paper, we propose the definition of data integrity in PSI and construct two authenticated PSI schemes by integrating Merkle Trees with state-of-the-art two-party volePSI and multi-party mPSI protocols. The resulting two-party authenticated PSI achieves communication complexity $\mathcal{O}(n \lambda+n \log n)$, aligning with the best-known unauthenticated PSI schemes, while the multi-party construction is $\mathcal{O}(n \kappa+n \log n)$ which introduces additional overhead due to Merkle tree inclusion proofs. Due to the incorporation of integrity verification, our authenticated schemes incur higher costs compared to state-of-the-art unauthenticated schemes. We also provide efficient implementations of our protocols and discuss potential improvements, including alternative authentication blocks.

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arXiv2025

RainFusion: Adaptive Video Generation Acceleration via Multi-Dimensional Visual Redundancy

Video generation using diffusion models is highly computationally intensive, with 3D attention in Diffusion Transformer (DiT) models accounting for over 80\% of the total computational resources. In this work, we introduce {\bf RainFusion}, a novel training-free sparse attention method that exploits inherent sparsity nature in visual data to accelerate attention computation while preserving video quality. Specifically, we identify three unique sparse patterns in video generation attention calculations--Spatial Pattern, Temporal Pattern and Textural Pattern. The sparse pattern for each attention head is determined online with negligible overhead (\textasciitilde\,0.2\%) with our proposed {\bf ARM} (Adaptive Recognition Module) during inference. Our proposed {\bf RainFusion} is a plug-and-play method, that can be seamlessly integrated into state-of-the-art 3D-attention video generation models without additional training or calibration. We evaluate our method on leading open-sourced models including HunyuanVideo, OpenSoraPlan-1.2 and CogVideoX-5B, demonstrating its broad applicability and effectiveness. Experimental results show that RainFusion achieves over {\bf 2$\times$} speedup in attention computation while maintaining video quality, with only a minimal impact on VBench scores (-0.2\%).

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arXiv2025

MacWilliams Theory over Zk and nu-functions over Lattices

Continuing previous works on MacWilliams theory over codes and lattices, a generalization of the MacWilliams theory over $\mathbb{Z}_k$ for $m$ codes is established, and the complete weight enumerator MacWilliams identity also holds for codes over the finitely generated rings $\mathbb{Z}_k[\xi]$. In the context of lattices, the analogy of the MacWilliams identity associated with nu-function was conjectured by Sol\'{e} in 1995, and we present a new formula for nu-function over the lattices associated with a ternary code, which is rather different from the original conjecture. Furthermore, we provide many counterexamples to show that the Sol\'{e} conjecture never holds in the general case, except for the lattices associated with a binary code.

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arXiv2025

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function

In this paper, we study linear codes over $\mathbb{Z}_k$ based on lattices and theta functions. We obtain the complete weight enumerators MacWilliams identity and the symmetrized weight enumerators MacWilliams identity based on the theory of theta function. We extend the main work by Bannai, Dougherty, Harada and Oura to the finite ring $\mathbb{Z}_k$ for any positive integer $k$ and present the complete weight enumerators MacWilliams identity in genus $g$. When $k=p$ is a prime number, we establish the relationship between the theta function of associated lattices over a cyclotomic field and the complete weight enumerators with Hamming weight of codes, which is an analogy of the results by G. Van der Geer and F. Hirzebruch since they showed the identity with the Lee weight enumerators.

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arXiv2025

Authenticated Sublinear Quantum Private Information Retrieval

This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities, the authors establish tighter bounds for information-theoretic security, demonstrating that quantum protocols inherently outperform classical counterparts in balancing privacy and efficiency. Also explores symmetric Quantum Private Information Retrieval (QPIR) protocols that achieve sub-linear communication complexity while ensuring robustness against specious adversaries: A post-quantum cryptography based protocol that can be authenticated for the specious server; A ring-LWE-based protocol for post-quantum security in a single-server setting, ensuring robustness against quantum attacks; A multi-server protocol optimized for hardware practicality, reducing implementation overhead while maintaining sub-linear efficiency. These protocols address critical gaps in secure database queries, offering exponential communication improvements over classical linear-complexity methods. The work also analyzes security trade-offs under quantum specious adversaries, providing theoretical guarantees for privacy and correctness.

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arXiv2025

Semigroup-homomorphic Signature

In 2002, Johnson et al. posed an open problem at the Cryptographers' Track of the RSA Conference: how to construct a secure homomorphic signature on a semigroup, rather than on a group. In this paper, we introduce, for the first time, a semigroup-homomorphic signature scheme. Under certain conditions, we prove that the security of this scheme is based on the hardness of the Short Integer Solution (SIS) problem and is tightly secure. Furthermore, we extend it to a linear semigroup-homomorphic signature scheme over lattices, and this scheme can also ensure privacy.

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arXiv2024

Linearly Homomorphic Signature with Tight Security on Lattice

Constructing cryptographic schemes with tight or almost-tight security has long been one of the central problems in theoretical cryptography. At ASIACRYPT 2016, Boyen and Li posed an open problem: whether it is possible to construct a homomorphic signature scheme with tight or almost-tight security under the Short Integer Solution (SIS) assumption in the standard model. In 2024, Chen achieved the first construction with almost-tight security under a weaker security model. To further achieve tight security in the standard model, this paper introduces a new security model whose security requirements are weaker than those of the standard adaptive model but stronger than the model adopted by Chen. Under this model, we construct a linearly homomorphic signature scheme with tight security.

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arXiv2024

Deep unrolled primal dual network for TOF-PET list-mode image reconstruction

Time-of-flight (TOF) information provides more accurate location data for annihilation photons, thereby enhancing the quality of PET reconstruction images and reducing noise. List-mode reconstruction has a significant advantage in handling TOF information. However, current advanced TOF PET list-mode reconstruction algorithms still require improvements when dealing with low-count data. Deep learning algorithms have shown promising results in PET image reconstruction. Nevertheless, the incorporation of TOF information poses significant challenges related to the storage space required by deep learning methods, particularly for the advanced deep unrolled methods. In this study, we propose a deep unrolled primal dual network for TOF-PET list-mode reconstruction. The network is unrolled into multiple phases, with each phase comprising a dual network for list-mode domain updates and a primal network for image domain updates. We utilize CUDA for parallel acceleration and computation of the system matrix for TOF list-mode data, and we adopt a dynamic access strategy to mitigate memory consumption. Reconstructed images of different TOF resolutions and different count levels show that the proposed method outperforms the LM-OSEM, LM-EMTV, LM-SPDHG,LM-SPDHG-TV and FastPET method in both visually and quantitative analysis. These results demonstrate the potential application of deep unrolled methods for TOF-PET list-mode data and show better performance than current mainstream TOF-PET list-mode reconstruction algorithms, providing new insights for the application of deep learning methods in TOF list-mode data. The codes for this work are available at https://github.com/RickHH/LMPDnet

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arXiv2024

On the MacWilliams Theorem over Codes and Lattices

Analogies between codes and lattices have been extensively studied for the last decades, in this dictionary, the MacWilliams identity is the finite analog of the Jacobi-Poisson formula of the Theta function. Motivated by the random theory of lattices, the statistical significance of MacWilliams theorem is considered, indeed, MacWilliams distribution provides a finite analog of the classical Gauss distribution. In particular, the MacWilliams distribution over quotient space of a code is statistical close to the uniform distribution. In the respect of lattices, the analogy of MacWilliams identity associated with nu-function was conjectured by Sole in 1995. We give an answer to this problem in positive.

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arXiv2024

Reusable Architecture Growth for Continual Stereo Matching

The remarkable performance of recent stereo depth estimation models benefits from the successful use of convolutional neural networks to regress dense disparity. Akin to most tasks, this needs gathering training data that covers a number of heterogeneous scenes at deployment time. However, training samples are typically acquired continuously in practical applications, making the capability to learn new scenes continually even more crucial. For this purpose, we propose to perform continual stereo matching where a model is tasked to 1) continually learn new scenes, 2) overcome forgetting previously learned scenes, and 3) continuously predict disparities at inference. We achieve this goal by introducing a Reusable Architecture Growth (RAG) framework. RAG leverages task-specific neural unit search and architecture growth to learn new scenes continually in both supervised and self-supervised manners. It can maintain high reusability during growth by reusing previous units while obtaining good performance. Additionally, we present a Scene Router module to adaptively select the scene-specific architecture path at inference. Comprehensive experiments on numerous datasets show that our framework performs impressively in various weather, road, and city circumstances and surpasses the state-of-the-art methods in more challenging cross-dataset settings. Further experiments also demonstrate the adaptability of our method to unseen scenes, which can facilitate end-to-end stereo architecture learning and practical deployment.

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arXiv2023

An Unbounded Fully Homomorphic Encryption Scheme Based on Ideal Lattices and Chinese Remainder Theorem

We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos \cite{32} in 1978, and to some new problems appeared in Peikert \cite{28} as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work \cite{14,15} of Gentry in 2009. Gentry's bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of unbounded FHE scheme is straightforward and noise-free that can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.

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arXiv2021

A Generalization of Cyclic Code and Applications to Public Key Cryptosystems

In this paper, we define and discuss ϕ-cyclic code, which may be regarded as a general form of the ordinary cyclic code. As applications, we explain how to extend two public key encryption schemes, one is McEliece and Niederriter's cryptosystem of which is based on error-correcting code theory. Another one is NTRU public key cryptosystem of which is based on polynomial ring theory. The main purpose of this paper is to give a more general construction of NTRU based on ideal matrices and q-ary lattice theory.

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arXiv2021

Cyclic Lattices, Ideal Lattices and Bounds for the Smoothing Parameter

Cyclic lattices and ideal lattices were introduced by Micciancio in \cite{D2}, Lyubashevsky and Micciancio in \cite{L1} respectively, which play an efficient role in Ajtai's construction of a collision resistant Hash function (see \cite{M1} and \cite{M2}) and in Gentry's construction of fully homomorphic encryption (see \cite{G}). Let $R=Z[x]/\langle ϕ(x)\rangle$ be a quotient ring of the integer coefficients polynomials ring, Lyubashevsky and Micciancio regarded an ideal lattice as the correspondence of an ideal of $R$, but they neither explain how to extend this definition to whole Euclidean space $\mathbb{R}^n$, nor exhibit the relationship of cyclic lattices and ideal lattices. In this paper, we regard the cyclic lattices and ideal lattices as the correspondences of finitely generated $R$-modules, so that we may show that ideal lattices are actually a special subclass of cyclic lattices, namely, cyclic integer lattices. In fact, there is a one to one correspondence between cyclic lattices in $\mathbb{R}^n$ and finitely generated $R$-modules (see Theorem \ref{th4} below). On the other hand, since $R$ is a Noether ring, each ideal of $R$ is a finitely generated $R$-module, so it is natural and reasonable to regard ideal lattices as a special subclass of cyclic lattices (see corollary \ref{co3.4} below). It is worth noting that we use more general rotation matrix here, so our definition and results on cyclic lattices and ideal lattices are more general forms. As application, we provide cyclic lattice with an explicit and countable upper bound for the smoothing parameter (see Theorem \ref{th5} below). It is an open problem that is the shortest vector problem on cyclic lattice NP-hard? (see \cite{D2}). Our results may be viewed as a substantial progress in this direction.

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