arXiv subjects

Cong Ling

Publications and source records attributed to Cong Ling.

At least 19 recordsLinked to original sources

arXiv2026

Improved Dual Attack and Trapdoor Sampling via Quantum Rejection Sampling

In this work, we revisit the dual attack and GPV trapdoor sampling, focusing on the lattice Gaussian sampling term, which can be a significant bottleneck in the overall complexity. We show that this sampling step can be quantumly accelerated by combining the lower bound underlying Wang and Ling's analysis of Klein's algorithm with the quantum rejection sampling (QRS) framework proposed by Ozols et al. Specifically, this lower bound gives precisely the pointwise domination condition required for quantum rejection sampling when given coherent oracle access to a truncated Klein proposal distribution, which yields a quantum procedure for preparing the truncated dual $q$-ary lattice Gaussian with a quadratic reduction in the sampling complexity. The truncation radius is chosen so that the truncated distribution is negligibly close to the full lattice Gaussian in total variation distance. Substituting this sampler into the dual attack framework results in reduced overall attack-cost estimates. Compared with Pouly and Shen's modern dual attack under the same parameter choices, our estimates reduce the attack cost by $9$, $4$, and $13$ bits for Kyber-512, Kyber-768, and Kyber-1024, respectively. We also report the corresponding estimates with modulus switching. Finally, by replacing the Markov chain Monte Carlo (MCMC) sampler with the QRS algorithm, we achieve a similar quadratic speedup in the GPV signing process.

quant-ph↗

arXiv2026

Construction $\pi_A$ over Multiquadratic Fields for Compound Block-Fading Wiretap Channels

We construct multilevel lattice codes from multiquadratic number fields for the compound block-fading wiretap channel. More precisely, we specialize Construction $\pi_A$ over the ring of integers $\mathcal{O}_K$ and exploit rational primes that split completely in $K$ to obtain a Chinese Remainder Theorem (CRT) decomposition into small residue alphabets, notably binary, which enables multistage decoding. The resulting nested lattices fit into the algebraic Construction A framework and, when combined with discrete Gaussian shaping and flatness-factor bounds, provide universal reliability for the legitimate receiver and strong secrecy uniformly over the eavesdropper compound set.

cs.IT↗

arXiv2025

Sphere Decoding Revisited

In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding (ESD) is proposed, which is essentially the same with the classic Fincke-Pohst sphere decoding but characterizes the sphere radius $D>0$ with two new parameters named as initial searching size $K>1$ and deviation factor $\sigma>0$. By fixing $\sigma$ properly, we show that given the sphere radius $D\triangleq\sigma\sqrt{2\ln K}$, the complexity of ESD in terms of the number of visited nodes is upper bounded by $|S|<nK$, thus resulting in an explicit and tractable decoding trade-off solely controlled by $K$. To the best of our knowledge, this is the first time that the complexity of sphere decoding is exactly specified, where considerable decoding potential can be explored from it. After that, two enhancement mechanisms named as normalized weighting and candidate protection are proposed to further upgrade the ESD algorithm. On one hand, given the same setups of $K$ and $\sigma$, a larger sphere radius is achieved, indicating a better decoding trade-off. On the other hand, the proposed ESD algorithm is generalized, which bridges suboptimal and optimal decoding performance through the flexible choice of $K$. Finally, further performance optimization and complexity reduction with respect to ESD are also derived, and the introduced tractable and flexible decoding trade-off is verified through large-scale MIMO detection.

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arXiv2025

Information Theoretic Learning for Diffusion Models with Warm Start

Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited theoretical understanding. In this paper, we derive a tighter likelihood bound for noise driven models to improve both the accuracy and efficiency of maximum likelihood learning. Our key insight extends the classical KL divergence Fisher information relationship to arbitrary noise perturbations, going beyond the Gaussian assumption and enabling structured noise distributions. This formulation allows flexible use of randomized noise distributions that naturally account for sensor artifacts, quantization effects, and data distribution smoothing, while remaining compatible with standard diffusion training. Treating the diffusion process as a Gaussian channel, we further express the mismatched entropy between data and model, showing that the proposed objective upper bounds the negative log-likelihood (NLL). In experiments, our models achieve competitive NLL on CIFAR-10 and SOTA results on ImageNet across multiple resolutions, all without data augmentation, and the framework extends naturally to discrete data.

cs.IT↗

arXiv2025

Generalized Score Matching: Bridging $f$-Divergence and Statistical Estimation Under Correlated Noise

Relative Fisher information, also known as score matching, is a recently introduced learning method for parameter estimation. Fundamental relations between relative entropy and score matching have been established in the literature for scalar and isotropic Gaussian channels. This paper demonstrates that such relations hold for a much larger class of observation models. We introduce the vector channel where the perturbation is non-isotropic Gaussian noise. For such channels, we derive new representations that connect the $f$-divergence between two distributions to the estimation loss induced by mismatch at the decoder. This approach not only unifies but also greatly extends existing results from both the isotropic Gaussian and classical relative entropy frameworks. Building on this generalization, we extend De Bruijn's identity to mismatched non-isotropic Gaussian models and demonstrate that the connections to generative models naturally follow as a consequence application of this new result.

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arXiv2025

Construction of Simultaneously Good Polar Codes and Polar Lattices

In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of such kind of lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.

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arXiv2024

Smoothing Linear Codes by R\'enyi Divergence and Applications to Security Reduction

The concept of the smoothing parameter plays a crucial role in both lattice-based and code-based cryptography, primarily due to its effectiveness in achieving nearly uniform distributions through the addition of noise. Recent research by Pathegama and Barg has determined the optimal smoothing bound for random codes under R\'enyi Divergence for any order $\alpha \in (1, \infty)$ \cite{pathegama2024r}. Considering the inherent complexity of encoding/decoding algorithms in random codes, our research introduces enhanced structural elements into these coding schemes. Specifically, this paper presents a novel derivation of the smoothing bound for random linear codes, maintaining the same order of R\'enyi Divergence and achieving optimality for any $\alpha\in (1,\infty)$. We extend this framework under KL Divergence by transitioning from random linear codes to random self-dual codes, and subsequently to random quasi-cyclic codes, incorporating progressively more structures. As an application, we derive an average-case to average-case reduction from the Learning Parity with Noise (LPN) problem to the average-case decoding problem. This reduction aligns with the parameter regime in \cite{debris2022worst}, but uniquely employs R\'enyi divergence and directly considers Bernoulli noise, instead of combining ball noise and Bernoulli noise.

cs.IT↗

arXiv2024

On the quantization goodness of polar lattices

In this work, we prove that polar lattices, when tailored for lossy compression, are quantization-good in the sense that their normalized second moments approach $\frac{1}{2\pi e}$ as the dimension of lattices increases. It has been predicted by Zamir et al. \cite{ZamirQZ96} that the Entropy Coded Dithered Quantization (ECDQ) system using quantization-good lattices can achieve the rate-distortion bound of i.i.d. Gaussian sources. In our previous work \cite{LingQZ}, we established that polar lattices are indeed capable of attaining the same objective. It is reasonable to conjecture that polar lattices also demonstrate quantization goodness in the context of lossy compression. This study confirms this hypothesis.

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arXiv2024

Multilevel lattice codes from Hurwitz quaternion integers

This work presents an extension of the Construction $\pi_A$ lattices proposed in \cite{huang2017construction}, to Hurwitz quaternion integers. This construction is provided by using an isomorphism from a version of the Chinese remainder theorem applied to maximal orders in contrast to natural orders in prior works. Exploiting this map, we analyze the performance of the resulting multilevel lattice codes, highlight via computer simulations their notably reduced computational complexity provided by the multistage decoding. Moreover it is shown that this construction effectively attain the Poltyrev-limit.

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arXiv2023

Unit Reducible Cyclotomic Fields

In this paper, we continue the study of unit reducible fields as introduced in \cite{LPL23} for the special case of cyclotomic fields. Specifically, we deduce that the cyclotomic fields of conductors $2,3,5,7,8,9,12,15$ are all unit reducible, and show that any cyclotomic field of conductor $N$ is not unit reducible if $2^4, 3^3, 5^2, 7^2, 11^2$ or any prime $p \geq 13$ divide $N$, meaning the unit reducible cyclotomic fields are finite in number. Finally, if $a$ is a totally positive element of a cyclotomic field, we show that for all equivalent $a^\prime$, the discrepancy between $\trace_{K/\mathbb{Q}}(a^\prime)$ and the shortest nonzero element of the quadratic form $\trace_{K/\mathbb{Q}}(axx^*)$ where $x$ is taken from the ring of integers tends to infinity as the conductor $N$ goes to infinity.

math.NT↗

arXiv2023

PAC Codes for Source and Joint Source-Channel Coding

Polarization-adjusted convolutional (PAC) codes, as a concatenated coding scheme based on polar codes, is able to approach the finite-length bound of binary-input AWGN channel at short blocklengths. In this paper, we extend PAC codes to the fields of source coding and joint source-channel coding and show that they can also approach the corresponding finite-length bounds at short blocklengths.

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arXiv2023

Efficient Lattice Hamiltonian Encoding for the Shortest Vector Problem

The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed that the structure of these lattices cannot be exploited by quantum or classical algorithms attempting to find short vectors. In this work, we focus on the structure of the lattices used in PQC protocols - nega-cyclic (and cyclic)lattices - and provide a quantum algorithmic framework that efficiently encodes the structured lattices into Hamiltonians by exploiting their underlying symmetries. The efficient encoding substantially reduces the dimension of the corresponding Hilbert space by limiting it to a relevant subspace where short vectors are likely to be found - leading to significant savings in quantum resources (e.g. qubit count and circuit depth) required to implement a quantum algorithm for finding short vectors. We analytically prove the efficient encoding procedure and benchmark the proposed framework using the variational quantum eigensolver, demonstrating improved results with reduced quantum resources.

quant-ph↗

arXiv2023

Quantum algorithmic solutions to the shortest vector problem on simulated coherent Ising machines

Quantum computing poses a threat to contemporary cryptosystems, with advances to a state in which it will cause problems predicted for the next few decades. Many of the proposed cryptosystems designed to be quantum-secure are based on the Shortest Vector Problem and related problems. In this paper we use the Quadratic Unconstrained Binary Optimisation formulation of the Shortest Vector Problem implemented as a quantum Ising model on a simulated Coherent Ising Machine, showing progress towards solving SVP for three variants of the algorithm.

quant-ph↗

arXiv2022

Lattice Codes for Lattice-Based PKE

Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either naive modulation or its concatenation with error correction codes (ECC). This paper shows that lattice coding, as a joint ECC and modulation technique, can substitute the naive modulation in existing lattice-based PKEs to enjoy better correction performance. We begin by modeling the FrodoPKE protocol as a noisy point-to-point communication system, where the communication channel is similar to the additive white Gaussian noise (AWGN) channel. To employ lattice codes for this special channel that hinges on hypercube shaping, we propose an efficient labeling function that converts between binary information bits and lattice codewords. The parameter sets of FrodoPKE are improved towards either higher security levels or smaller ciphertext sizes. For example, the proposed Frodo-1344-E$_\text{8}$ has a 10-bit classical security gain over Frodo-1344.

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arXiv2022

Wang Algebra: From Theory to Practice

Wang algebra was initiated by Ki-Tung Wang as a short-cut method for the analysis of electrical networks. It was later popularized by Duffin and has since found numerous applications in electrical engineering and graph theory. This is a semi-tutorial paper on Wang algebra, its history, and modern applications. We expand Duffin's historic notes on Wang algebra to give a full account of Ki-Tung Wang's life. A short proof of Wang algebra using group theory is presented. We exemplify the usefulness of Wang algebra in the design of T-coils. Bridged T-coils give a significant advantage in bandwidth, and were widely adopted in Tektronix oscilloscopes, but design details were guarded as a trade secret. The derivation presented in this paper, based on Wang algebra, is more general and simpler than those reported in literature. This novel derivation has not been shared with the public before.

math.HO↗

arXiv2022

Algorithms and Bounds for Complex and Quaternionic Lattices With Application to MIMO Transmission

Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are considered. However, in communications, complex-valued processing is usually of interest. Besides, by the use of dual-polarized transmission as well as by the combination of two time slots or frequencies, four-dimensional (quaternion-valued) approaches become more and more important. Hence, to account for this fact, well-known lattice algorithms and related concepts are generalized in this work. To this end, a brief review of complex arithmetic, including the sets of Gaussian and Eisenstein integers, and an introduction to quaternion-valued numbers, including the sets of Lipschitz and Hurwitz integers, are given. On that basis, generalized variants of two important algorithms are derived: first, of the polynomial-time LLL algorithm, resulting in a reduced basis of a lattice by performing a special variant of the Euclidean algorithm defined for matrices, and second, of an algorithm to calculate the successive minima - the norms of the shortest independent vectors of a lattice - and its related lattice points. Generalized bounds for the quality of the particular results are established and the asymptotic complexities of the algorithms are assessed. These findings are extensively compared to conventional real-valued processing. It is shown that the generalized approaches outperform their real-valued counterparts in complexity and/or quality aspects. Moreover, the application of the generalized algorithms to MIMO communications is studied, particularly in the field of lattice-reduction-aided and integer-forcing equalization.

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arXiv2022

A New Bound for the Orthogonality Defect of HKZ Reduced Lattices

In this work, we determine a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension $3$. Using this result, we determine a general upper bound for the orthogonality defect of HKZ reduced bases of arbitrary rank. This upper bound seems to be sharper than existing bounds in literature, such as the one determined by Lagarias, Lenstra and Schnorr.

math.NT↗

arXiv2022

Unit Reducible Fields and Perfect Unary Forms

In this paper, we introduce the notion of unit reducibility for number fields, that is, number fields in which all positive unary forms attain their nonzero minimum at a unit. Furthermore, we investigate the link between unit reducibility and the number of homothety classes of perfect unary forms for a given number field, and prove an open conjecture about the number of classes of perfect unary forms in real quadratic fields, stated by D. Yasaki.

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