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Honggang Hu

Publications and source records attributed to Honggang Hu.

15 recordsLinked to original sources
arXiv2026

Subset Balancing and Generalized Subset Sum via Lattices

We study the Subset Balancing problem: given $x \in \mathbb{Z}^n$ and a coefficient set $C \subseteq \mathbb{Z}$, find a nonzero vector $c \in C^n$ such that $c\cdot x = 0$. The standard meet-in-the-middle algorithm runs in time $\tilde{O}(|C|^{n/2})$, and recent improvements (SODA 2022, Chen, Jin, Randolph, and Servedio; STOC 2026, Randolph and W\k{e}grzycki) beyond this barrier apply mainly when $d$ is constant. We give a reduction from Subset Balancing with $C = \{-d, \dots, d\}$ to a single instance of SVP$_{\infty}$ in dimension $n+1$. Instantiating this reduction with the best known $\ell_\infty$-SVP algorithms yields a deterministic $\tilde{O}((6\sqrt{2\pi e})^n)$-time algorithm and a randomized $\tilde{O}(2^{2.443n})$-time algorithm. The exponent depends only on $n$, improving on meet-in-the-middle for all $d\ge 15$. For sufficiently large $d$ we also obtain a polynomial-time algorithm. The reduction extends from the box constraint $[-d,d]^n$ to any centrally symmetric convex body $K\subseteq\mathbb{R}^n$, giving deterministic time $\tilde{O}(2^{c_K n})$ for a constant $c_K$ depending only on the shape of $K$. We further study the Generalized Subset Sum problem of finding $c \in C^n$ such that $c \cdot x = \tau$. For $C = \{-d, \dots, d\}$ or $C = \{-d,\dots,d\}\setminus\{0\}$, we reduce the worst-case problem to CVP$_{\infty}$ in dimension $n+1$. We observe that distances in our lattice take only integer values, so an approximate CVP$_{\infty}$ oracle still suffices, yielding a deterministic worst-case algorithm running in time $2^{O(n\log\log d)}$. In the average-case setting, we demonstrate that for both coefficient sets the embedded CVP$_{\infty}$ instance satisfies a bounded-distance promise with high probability, removing the $\log\log d$ factor altogether and obtaining a deterministic algorithm running in time $\tilde{O}((18\sqrt{2\pi e})^n)$.

cs.DS↗
arXiv2025

On Factoring and Power Divisor Problems via Rank-3 Lattices and the Second Vector

We propose a deterministic algorithm based on Coppersmith's method that employs a rank-3 lattice to address factoring-related problems. An interesting aspect of our approach is that we utilize the second vector in the LLL-reduced basis to avoid trivial collisions in the Baby-step Giant-step method, rather than the shortest vector as is commonly used in the literature. Our results are as follows: 1. Compared to the result by Harvey and Hittmeir (Math. Comp. 91 (2022), 1367 - 1379), who achieved a complexity of O( N^(1/5) log^(16/5) N / (log log N)^(3/5)) for factoring a semiprime N = pq, we demonstrate that in the balanced p and q case, the complexity can be improved to O( N^(1/5) log^(13/5) N / (log log N)^(3/5) ). 2. For factoring sums and differences of powers, that is, numbers of the form N = a^n plus or minus b^n, we improve Hittmeir's result (Math. Comp. 86 (2017), 2947 - 2954) from O( N^(1/4) log^(3/2) N ) to O( N^(1/5) log^(13/5) N ). 3. For the problem of finding r-power divisors, that is, finding all integers p such that p^r divides N, Harvey and Hittmeir (Proceedings of ANTS XV, Research in Number Theory 8 (2022), no. 4, Paper No. 94) recently directly applied Coppersmith's method and achieved a complexity of O( N^(1/(4r)) log^(10+epsilon) N / r^3 ). By using faster LLL-type algorithms and sieving on small primes, we improve their result to O( N^(1/(4r)) log^(7+3 epsilon) N / ((log log N minus log(4r)) r^(2+epsilon)) ). The worst-case running time for their algorithm occurs when N = p^r q with q on the order of N^(1/2). By focusing on this case and employing our rank-3 lattice approach, we achieve a complexity of O( r^(1/4) N^(1/(4r)) log^(5/2) N ). In conclusion, we offer a new perspective on these problems, which we hope will provide further insights.

math.NT↗
arXiv2024

Mixture-of-Noises Enhanced Forgery-Aware Predictor for Multi-Face Manipulation Detection and Localization

With the advancement of face manipulation technology, forgery images in multi-face scenarios are gradually becoming a more complex and realistic challenge. Despite this, detection and localization methods for such multi-face manipulations remain underdeveloped. Traditional manipulation localization methods either indirectly derive detection results from localization masks, resulting in limited detection performance, or employ a naive two-branch structure to simultaneously obtain detection and localization results, which cannot effectively benefit the localization capability due to limited interaction between two tasks. This paper proposes a new framework, namely MoNFAP, specifically tailored for multi-face manipulation detection and localization. The MoNFAP primarily introduces two novel modules: the Forgery-aware Unified Predictor (FUP) Module and the Mixture-of-Noises Module (MNM). The FUP integrates detection and localization tasks using a token learning strategy and multiple forgery-aware transformers, which facilitates the use of classification information to enhance localization capability. Besides, motivated by the crucial role of noise information in forgery detection, the MNM leverages multiple noise extractors based on the concept of the mixture of experts to enhance the general RGB features, further boosting the performance of our framework. Finally, we establish a comprehensive benchmark for multi-face detection and localization and the proposed \textit{MoNFAP} achieves significant performance. The codes will be made available.

cs.CV↗
arXiv2024

Multi-spectral Class Center Network for Face Manipulation Detection and Localization

As deepfake content proliferates online, advancing face manipulation forensics has become crucial. To combat this emerging threat, previous methods mainly focus on studying how to distinguish authentic and manipulated face images. Although impressive, image-level classification lacks explainability and is limited to specific application scenarios, spurring recent research on pixel-level prediction for face manipulation forensics. However, existing forgery localization methods suffer from exploring frequency-based forgery traces in the localization network. In this paper, we observe that multi-frequency spectrum information is effective for identifying tampered regions. To this end, a novel Multi-Spectral Class Center Network (MSCCNet) is proposed for face manipulation detection and localization. Specifically, we design a Multi-Spectral Class Center (MSCC) module to learn more generalizable and multi-frequency features. Based on the features of different frequency bands, the MSCC module collects multi-spectral class centers and computes pixel-to-class relations. Applying multi-spectral class-level representations suppresses the semantic information of the visual concepts which is insensitive to manipulated regions of forgery images. Furthermore, we propose a Multi-level Features Aggregation (MFA) module to employ more low-level forgery artifacts and structural textures. Meanwhile, we conduct a comprehensive localization benchmark based on pixel-level FF++ and Dolos datasets. Experimental results quantitatively and qualitatively demonstrate the effectiveness and superiority of the proposed MSCCNet. We expect this work to inspire more studies on pixel-level face manipulation localization. The codes are available (https://github.com/miaoct/MSCCNet).

cs.CV↗
arXiv2021

Two Problems about Monomial Bent Functions

In 2008, Langevin and Leander determined the dual function of three classes of monomial bent functions with the help of Stickelberger's theorem: Dillon, Gold and Kasami. In their paper, they proposed one very strong condition such that their method works, and showed that both Gold exponent and Kasami exponent satisfy this condition. In 2018, Pott {\em et al.} investigated the issue of vectorial functions with maximal number of bent components. They found one class of binomial functions which attains the upper bound. They also proposed an open problem regarding monomial function with maximal number of bent components. In this paper, we obtain an interesting result about the condition of Langevin and Leander, and solve the open problem of Pott {\em et al.}. Specifically, we show that: 1) for a monomial bent function over $\mathbb{F}_{2^{2k}}$, if the exponent satisfies the first part of the condition of Langevin and Leander, then it satisfies the entire condition; 2) $x^{2^k+1}$ is the only monomial function over $\mathbb{F}_{2^{2k}}$ which has maximal number of bent components. Fortunately, as a consequence, we also solve an open problem of Ness and Helleseth in 2006.

cs.IT↗
arXiv2021

A Fast-Detection and Fault-Correction Algorithm against Persistent Fault Attack

Persistent Fault Attack (PFA) is a recently proposed Fault Attack (FA) method in CHES 2018. It is able to recover full AES secret key in the Single-Byte-Fault scenario. It is demonstrated that classical FA countermeasures, such as Dual Modular Redundancy (DMR) and mask protection, are unable to thwart PFA. In this paper, we propose a fast-detection and faultcorrection algorithm to prevent PFA. We construct a fixed input and output pair to detect faults rapidly. Then we build two extra redundant tables to store the relationship between the adjacent elements in the S-box, by which the algorithm can correct the faulty elements in the S-box. Our experimental results show that our algorithm can effectively prevent PFA in both Single-ByteFault and Multiple-Bytes-Faults scenarios. Compared with the classical FA countermeasures, our algorithm has a much better effect against PFA. Further, the time cost of our algorithm is 40% lower than the classical FA countermeasures.

cs.CR↗
arXiv2021

Towards Strengthening Deep Learning-based Side Channel Attacks with Mixup

In recent years, various deep learning techniques have been exploited in side channel attacks, with the anticipation of obtaining more appreciable attack results. Most of them concentrate on improving network architectures or putting forward novel algorithms, assuming that there are adequate profiling traces available to train an appropriate neural network. However, in practical scenarios, profiling traces are probably insufficient, which makes the network learn deficiently and compromises attack performance. In this paper, we investigate a kind of data augmentation technique, called mixup, and first propose to exploit it in deep-learning based side channel attacks, for the purpose of expanding the profiling set and facilitating the chances of mounting a successful attack. We perform Correlation Power Analysis for generated traces and original traces, and discover that there exists consistency between them regarding leakage information. Our experiments show that mixup is truly capable of enhancing attack performance especially for insufficient profiling traces. Specifically, when the size of the training set is decreased to 30% of the original set, mixup can significantly reduce acquired attacking traces. We test three mixup parameter values and conclude that generally all of them can bring about improvements. Besides, we compare three leakage models and unexpectedly find that least significant bit model, which is less frequently used in previous works, actually surpasses prevalent identity model and hamming weight model in terms of attack results.

cs.CR↗
arXiv2020

Adversarial Attack Based Countermeasures against Deep Learning Side-Channel Attacks

Numerous previous works have studied deep learning algorithms applied in the context of side-channel attacks, which demonstrated the ability to perform successful key recoveries. These studies show that modern cryptographic devices are increasingly threatened by side-channel attacks with the help of deep learning. However, the existing countermeasures are designed to resist classical side-channel attacks, and cannot protect cryptographic devices from deep learning based side-channel attacks. Thus, there arises a strong need for countermeasures against deep learning based side-channel attacks. Although deep learning has the high potential in solving complex problems, it is vulnerable to adversarial attacks in the form of subtle perturbations to inputs that lead a model to predict incorrectly. In this paper, we propose a kind of novel countermeasures based on adversarial attacks that is specifically designed against deep learning based side-channel attacks. We estimate several models commonly used in deep learning based side-channel attacks to evaluate the proposed countermeasures. It shows that our approach can effectively protect cryptographic devices from deep learning based side-channel attacks in practice. In addition, our experiments show that the new countermeasures can also resist classical side-channel attacks.

cs.CR↗
arXiv2020

An Enhanced Convolutional Neural Network in Side-Channel Attacks and Its Visualization

In recent years, the convolutional neural networks (CNNs) have received a lot of interest in the side-channel community. The previous work has shown that CNNs have the potential of breaking the cryptographic algorithm protected with masking or desynchronization. Before, several CNN models have been exploited, reaching the same or even better level of performance compared to the traditional side-channel attack (SCA). In this paper, we investigate the architecture of Residual Network and build a new CNN model called attention network. To enhance the power of the attention network, we introduce an attention mechanism - Convolutional Block Attention Module (CBAM) and incorporate CBAM into the CNN architecture. CBAM points out the informative points of the input traces and makes the attention network focus on the relevant leakages of the measurements. It is able to improve the performance of the CNNs. Because the irrelevant points will introduce the extra noises and cause a worse performance of attacks. We compare our attention network with the one designed for the masking AES implementation called ASCAD network in this paper. We show that the attention network has a better performance than the ASCAD network. Finally, a new visualization method, named Class Gradient Visualization (CGV) is proposed to recognize which points of the input traces have a positive influence on the predicted result of the neural networks. In another aspect, it can explain why the attention network is superior to the ASCAD network. We validate the attention network through extensive experiments on four public datasets and demonstrate that the attention network is efficient in different AES implementations.

cs.CR↗
arXiv2020

Enhancing the Performance of Practical Profiling Side-Channel Attacks Using Conditional Generative Adversarial Networks

Recently, many profiling side-channel attacks based on Machine Learning and Deep Learning have been proposed. Most of them focus on reducing the number of traces required for successful attacks by optimizing the modeling algorithms. In previous work, relatively sufficient traces need to be used for training a model. However, in the practical profiling phase, it is difficult or impossible to collect sufficient traces due to the constraint of various resources. In this case, the performance of profiling attacks is inefficient even if proper modeling algorithms are used. In this paper, the main problem we consider is how to conduct more efficient profiling attacks when sufficient profiling traces cannot be obtained. To deal with this problem, we first introduce the Conditional Generative Adversarial Network (CGAN) in the context of side-channel attacks. We show that CGAN can generate new traces to enlarge the size of the profiling set, which improves the performance of profiling attacks. For both unprotected and protected cryptographic algorithms, we find that CGAN can effectively learn the leakage of traces collected in their implementations. We also apply it to different modeling algorithms. In our experiments, the model constructed with the augmented profiling set can reduce the required attack traces by more than half, which means the generated traces can provide useful information as the real traces.

cs.CR↗
arXiv2017

New Classes of Ternary Bent Functions from the Coulter-Matthews Bent Functions

It has been an active research issue for many years to construct new bent functions. For $k$ odd with $\gcd(n, k)=1$, and $a\in\mathbb{F}_{3^n}^{*}$, the function $f(x)=Tr(ax^{\frac{3^k+1}{2}})$ is weakly regular bent over $\mathbb{F}_{3^n}$, where $Tr(\cdot):\mathbb{F}_{3^n}\rightarrow\mathbb{F}_3$ is the trace function. This is the well-known Coulter-Matthews bent function. In this paper, we determine the dual function of $f(x)$ completely. As a consequence, we find many classes of ternary bent functions not reported in the literature previously. Such bent functions are not quadratic if $k>1$, and have $\left(\left(\frac{1+\sqrt{5}}{2}\right)^{w+1}-\right.$ $\left.\left(\frac{1-\sqrt{5}}{2}\right)^{w+1}\right)/\sqrt{5}$ or $\left(\left(\frac{1+\sqrt{5}}{2}\right)^{n-w+1}-\right.$ $\left.\left(\frac{1-\sqrt{5}}{2}\right)^{n-w+1}\right)/\sqrt{5}$ trace terms, where $0<w<n$ and $wk\equiv 1\ (\bmod\;n)$. Among them, five special cases are especially interesting: for the case of $k=(n+1)/2$, the number of trace terms is $\left(\left(\frac{1+\sqrt{5}}{2}\right)^{n-1}-\right.$ $\left.\left(\frac{1-\sqrt{5}}{2}\right)^{n-1}\right)/\sqrt{5}$; for the case of $k=n-1$, the number of trace terms is $\left(\left(\frac{1+\sqrt{5}}{2}\right)^n-\right.$ $\left.\left(\frac{1-\sqrt{5}}{2}\right)^n\right)/\sqrt{5}$; for the case of $k=(n-1)/2$, the number of trace terms is $\left(\left(\frac{1+\sqrt{5}}{2}\right)^{n-1}-\right.$ $\left.\left(\frac{1-\sqrt{5}}{2}\right)^{n-1}\right)/\sqrt{5}$; for the case of $(n, k)=(5t+4, 4t+3)$ or $(5t+1, 4t+1)$ with $t\geq 1$, the number of trace terms is 8; and for the case of $(n, k)=(7t+6, 6t+5)$ or $(7t+1, 6t+1)$ with $t\geq 1$, the number of trace terms is 21. As a byproduct, we find new classes of ternary bent functions with only 8 or 21 trace terms.

cs.IT↗
arXiv2016

On the Dual of the Coulter-Matthews Bent Functions

For any bent function, it is very interesting to determine its dual function because the dual function is also bent in certain cases. For $k$ odd and $\gcd(n, k)=1$, it is known that the Coulter-Matthews bent function $f(x)=Tr(ax^{\frac{3^k+1}{2}})$ is weakly regular bent over $\mathbb{F}_{3^n}$, where $a\in\mathbb{F}_{3^n}^{*}$, and $Tr(\cdot):\mathbb{F}_{3^n}\rightarrow\mathbb{F}_3$ is the trace function. In this paper, we investigate the dual function of $f(x)$, and dig out an universal formula. In particular, for two cases, we determine the formula explicitly: for the case of $n=3t+1$ and $k=2t+1$ with $t\geq 2$, the dual function is given by $$Tr\left(-\frac{x^{3^{2t+1}+3^{t+1}+2}}{a^{3^{2t+1}+3^{t+1}+1}}-\frac{x^{3^{2t}+1}}{a^{-3^{2t}+3^{t}+1}}+\frac{x^{2}}{a^{-3^{2t+1}+3^{t+1}+1}}\right);$$ and for the case of $n=3t+2$ and $k=2t+1$ with $t\geq 2$, the dual function is given by $$Tr\left(-\frac{x^{3^{2t+2}+1}}{a^{3^{2t+2}-3^{t+1}+3}}-\frac{x^{2\cdot3^{2t+1}+3^{t+1}+1}}{a^{3^{2t+2}+3^{t+1}+1}}+\frac{x^2}{a^{-3^{2t+2}+3^{t+1}+3}}\right).$$ As a byproduct, we find two new classes of ternary bent functions with only three terms. Moreover, we also prove that in certain cases $f(x)$ is regular bent.

cs.IT↗
arXiv2014

Comments on "A New Method to Compute the 2-Adic Complexity of Binary Sequences"

We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the first main result by H. Xiong, L. Qu, and C. Li, IEEE Transactions on Information Theory, vol. 60, no. 4, pp. 2399-2406, Apr. 2014, and the main result by T. Tian and W. Qi, IEEE Transactions on Information Theory, vol. 56, no. 1, pp. 450-454, Jan. 2010.

cs.IT↗
arXiv2013

The Proof of Lin's Conjecture via the Decimation-Hadamard Transform

In 1998, Lin presented a conjecture on a class of ternary sequences with ideal 2-level autocorrelation in his Ph.D thesis. Those sequences have a very simple structure, i.e., their trace representation has two trace monomial terms. In this paper, we present a proof for the conjecture. The mathematical tools employed are the second-order multiplexing decimation-Hadamard transform, Stickelberger's theorem, the Teichmüller character, and combinatorial techniques for enumerating the Hamming weights of ternary numbers. As a by-product, we also prove that the Lin conjectured ternary sequences are Hadamard equivalent to ternary $m$-sequences.

cs.IT↗