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Yuzhou Fang

Publications and source records attributed to Yuzhou Fang.

At least 19 recordsLinked to original sources

Efficient Symbolic Execution of Software under Fault Attacks

We propose a symbolic execution method for analyzing the safety of software under fault attacks both accurately and efficiently. Fault attacks leverage physically injected hardware faults in an embedded system to break the safety of a software program. While there are existing methods for analyzing the impact of maliciously injected hardware faults on the embedded software, they suffer from inaccurate fault modeling and inefficient fault analysis. To overcome these limitations, we propose two novel techniques. First, we propose a new fault modeling technique that leverages automated program transformation to add symbolic variables to the original program, to accurately model the new program behavior induced by the injected faults. This new fault modeling approach has two advantages over existing techniques: (a) the fault-induced program behavior is closely related to what attackers exploit in practice and (b) the automatically transformed program may be analyzed by any downstream fault analysis algorithm. Second, we propose an efficient symbolic execution algorithm that is designed specifically for conducting fault analysis on the transformed program. It leverages two pruning techniques to mitigate path explosion. We have implemented the proposed method and evaluated it on a variety of benchmark programs. The experimental results show that our method significantly outperforms the state-of-the-art techniques. Compared to the current state-of-the-art, it is able to detect previously-missed safety violations and at the same time avoid bogus violations. Furthermore, compared to the baseline algorithm, our optimized symbolic execution algorithm can be orders-of-magnitude faster.

cs.SE

Gradient regularity for nonlocal double phase equations

This paper is devoted to investigating the interior $C^{1, \alpha}$ regularity of viscosity solutions to the nonlocal double phase equations $$ \int_{\mathbb{R}^d} \left(\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{d+sp}}+a(x,y)\frac{|u(x)-u(y)|^{q-2}(u(x)-u(y))}{|x-y|^{d+tq}}\right)dy=0, $$ where $2\le p\le q$, $0<s\le t<1$, and $a(x, y)\ge0$. By assuming the Lipschitz continuity of $a(\cdot)$, we show that the gradient of solution is H\"older continuous, provided the distance of $tq$ and $sp$ is suitably small. As a key ingredient to this conclusion, the Lipschitz property of solutions is also established under weaker assumptions on the modulating coefficient $a(\cdot)$, which is of independent interest. Our results develop a nonlocal counterpart of the gradient regularity theory for classical double phase problems due to Colombo \& Mingione [Arch. Ration. Mech. Anal., 2015] and solve the higher regularity issue raised by De Filippis \& Palatucci [J. Differential Equations, 2019]. The core challenges consist in precisely characterizing the subtle interaction among the pointwise behaviour of the coefficient $a(\cdot)$, the growth exponents and the differentiability orders.

math.AP

Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term

We investigate a class of degenerate fully nonlinear nonlocal elliptic equations with Hamiltonian terms. By precisely characterizing the interaction between the degeneracy law of equations and the growth behavior of the Hamiltonian terms, we establish the Lipschitz regularity of viscosity solutions by the Ishii-Lions method, and further show the gradient Hölder continuity for solutions via utilizing perturbation techniques. Additionally, under minimal assumptions on the degeneracy pattern, the $C^1$-differentiability property of solutions is explored as well.

math.AP

Tilt-to-length noise subtraction with pointing jitters from closed-loop dynamics for TianQin

TianQin is a proposed space-based mission for gravitational wave detection, employing a constellation of three drag-free satellites in high Earth orbits to form a laser interferometric observatory. A critical technical challenge is mitigating tilt-to-length (TTL) coupling noise, which is expected to be the third dominant noise source after laser frequency and clock noises. This noise is unavoidable in the presence of the residual angular movement of satellites, movable optical subassemblies (MOSAs), and test masses (TMs), and needs to be subtracted after reducing the first two types of noises using time-delay interferometry (TDI). Previous works have shown that TTL coupling coefficients can be estimated from the null TDI channel $ζ$ and used for noise subtraction in other combinations. However, it was found that correlated MOSA yaw jitters have a negative impact on the TTL calibration, and the effects of realistic residual angular jitters from drag-free and pointing control (DFPC) are yet to be investigated. In this paper, we use closed-loop DFPC simulations to generate more realistic jitters in the science mode and test TTL calibration capability. Our simulations reveal that rotating only one MOSA is more favorable, compared to symmetrically rotating two MOSAs, for enhancing the accuracy of TTL coefficient estimation, while employing only high-frequency data (0.1 - 1 Hz). Moreover, we propose two other methods to further improve estimation accuracy. Firstly, using different null channel combinations, such as $C_3^{14}$, enhances the least squares estimation accuracy even in the case of high correlations in MOSAs' yaw jitters. Secondly, injecting different sinusoidal artificial maneuvers to the six MOSAs also shows improvements. These methods can help TianQin to meet the 0.3 pm/Hz$^{1/2}$ requirement after the TTL noise subtraction.

gr-qc

Modeling coupled constellation dynamics for TianQin under self-gravity

TianQin is a dedicated geocentric mission for space-based gravitational wave (GW) detection. Among its core technologies, the drag-free and pointing control subsystem (DFPCS) - consisting of suspension, drag-free and pointing controls - keeps the two test masses (TMs) centered and aligned within their housings while maintaining drag-free conditions and precise telescope pointing along the laser-arm directions. This results in orbit-attitude coupled dynamics for the constellation. The coupling is made more prominent due to satellite self-gravity, which requires compensation from DFPCS and generally makes the satellites deviate from pure free-fall orbits. Previous studies assumed that the orbit and attitude dynamics could be decoupled in numerical simulation, neglecting the back-action from the closed-loop control to orbit propagation. To address this, we develop a comprehensive model that can propagate the full 9-body (6 TMs + 3 satellites, orbits and attitudes) dynamics inter-dependently under the inter-satellite pointing and drag-free conditions. This paper is threefold. First, we reassess the applicability of the two TMs and telescope pointing scheme to TianQin using the new model, and confirm the previous conclusion. Second, to meet the constellation stability requirements, it is found that the DC common self-gravity in the flight direction should be minimized, or kept close for the three satellites. Finally, we simulate the long-range light path between two TMs/satellites with a precision of sub-pm/Hz$^{1/2}$, and the results support the decoupling of the closed-loop dynamics and high-precision orbit for computational efficiency. The method is instrumental to other future missions where the orbit-attitude coupling needs careful consideration.

gr-qc

An Incremental Algorithm for Algebraic Program Analysis

We propose a method for conducting algebraic program analysis (APA) incrementally in response to changes of the program under analysis. APA is a program analysis paradigm that consists of two distinct steps: computing a path expression that succinctly summarizes the set of program paths of interest, and interpreting the path expression using a properly-defined semantic algebra to obtain program properties of interest. In this context, the goal of an incremental algorithm is to reduce the analysis time by leveraging the intermediate results computed before the program changes. We have made two main contributions. First, we propose a data structure for efficiently representing path expression as a tree together with a tree-based interpreting method. Second, we propose techniques for efficiently updating the program properties in response to changes of the path expression. We have implemented our method and evaluated it on thirteen Java applications from the DaCapo benchmark suite. The experimental results show that both our method for incrementally computing path expression and our method for incrementally interpreting path expression are effective in speeding up the analysis. Compared to the baseline APA and two state-of-the-art APA methods, the speedup of our method ranges from 160X to 4761X depending on the types of program analyses performed.

cs.PL

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of viscosity solutions according to different diffusion orders. More precisely, when the order of the fractional diffusion is sufficiently close to 2, we obtain Hölder continuity for the gradient of any viscosity solutions and further derive an improved gradient regularity estimate at the origin. For the order of the fractional diffusion in the interval $(1, 2)$, we prove that there is at least one solution of class $C^{1, α}_{\rm loc}$. Additionally, if the order of the fractional diffusion is in the interval $(0,1]$, the local Hölder continuity of solutions is inferred.

math.AP

Quantitative analysis and its applications for Keller-Segel type systems

In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented here has broad applications in determining large time behaviours of weak solutions and improving the regularity for models involving the $p$-Laplace operator. To demonstrate the applicability of our findings, we investigate the asymptotic stability of a chemotaxis model with nonlinear signal production and a chemotaxis-Navier-Stokes model with a logistic source. Additionally, within the context of $p$-Laplacian diffusion, we establish Hölder continuity for a chemotaxis-haptotaxis model and a chemotaxis-Stokes model.

math.AP

On the weak Harnack inequalities for nonlocal double phase problems

This paper is devoted to studying the weak Harnack inequalities for nonlocal double phase functionals by using expansion of positivity, whose prototype is $$ \iint_{\mathbb{R}^n\times\mathbb{R}^n} \left(\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}+a(x,y)\frac{|u(x)-u(y)|^q}{|x-y|^{n+tq}}\right) \,dxdy $$ with $a\ge0$ and $0<s\le t<1<p\le q$. The core of our approach is to establish several measure theoretical estimates based on the nonlocal Caccioppoli-type inequality, where the challenges consist in controlling subtle interaction between the pointwise behaviour of modulating coefficient and the growth exponents. Meanwhile, a quantitative boundedness result on the minimizer of such functionals is also discussed.

math.AP

On payload architecture and pointing control strategies for TianQin

TianQin is a proposed mission for space-based gravitational-wave detection that features a triangular constellation in circular high Earth orbits. The mission entails three drag-free controlled satellites and long-range laser interferometry with stringent beam pointing requirements at remote satellites. For the payload architecture and pointing control strategies, having two test masses per satellite, one for each laser arm, and rotating entire opto-mechanical assemblies (each consisting of a telescope, an optical bench, an inertial sensor, etc.) for constellation breathing angle compensation represent an important option for TianQin. In this paper, we examine its applicability from the perspectives of test mass and satellite control in the science mode, taking into account of perturbed orbits and orbital gravity gradients. First, based on the orbit-attitude coupling relationship, the required electrostatic forces and torques for the test mass suspension control are estimated and found to be sufficiently small for the acceleration noise budget. Further optimization favors configuring the centers of masses of the two test masses collinear and equidistant with the center of mass of the satellite, and slightly offsetting the assembly pivots from the electrode housing centers forward along the sensitive axes. Second, the required control forces and torques on the satellites are calculated, and thrust allocation solutions are found under the constraint of having a flat-top sunshield on the satellite with varying solar angles. The findings give a green light to adopting the two test masses and telescope pointing scheme for TianQin.

gr-qc

Regularity theory for nonlocal equations with general growth in the Heisenberg group

We deal with a wide class of generalized nonlocal $p$-Laplace equations, so-called nonlocal $G$-Laplace equations, in the Heisenberg framework. Under natural hypotheses on the $N$-function $G$, we provide a unified approach to investigate in the spirit of De Giorgi-Nash-Moser theory, some local properties of weak solutions to such kind of problems, involving boundedness, Hölder continuity and Harnack inequality. To this end, an improved nonlocal Caccioppoli-type estimate as the main auxiliary ingredient is exploited several times.

math.AP

Local regularity for nonlocal double phase equations in the Heisenberg group

We prove interior boundedness and Hölder continuity for the weak solutions of nonlocal double phase equations in the Heisenberg group $\mathbb{H}^n$. This solves a problem raised by Palatucci and Piccinini et. al. in 2022 and 2023 for nonlinear integro-differential problems in the Heisenberg group $\mathbb{H}^n$. Our proof of the a priori estiamtes bases on the spirit of De Giorgi-Nash-Moser theory, where the important ingredients are Caccioppoli-type inequality and Logarithmic estimate. To achieve this goal, we establish a new and crucial Sobolev-Poincaré type inequality in local domain, which may be of independent interest and potential applications.

math.AP

Local behaviour of the mixed local and nonlocal problems with nonstandard growth

We consider the mixed local and nonlocal functionals with nonstandard growth \begin{eqnarray*} u\mapsto\int_Ω(|Du|^p-f(x)u)\,dx+\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}\frac{|u(x)-u(y)|^q}{|x-y|^{N+sq}}\,dxdy \end{eqnarray*} with $1 sq$ in [De Filippis-Mingione, Math. Ann., https://doi.org/10.1007/s00208-022-02512-7].

math.AP

An Empirical Study of Blockchain System Vulnerabilities: Modules, Types, and Patterns

Blockchain, as a distributed ledger technology, becomes increasingly popular, especially for enabling valuable cryptocurrencies and smart contracts. However, the blockchain software systems inevitably have many bugs. Although bugs in smart contracts have been extensively investigated, security bugs of the underlying blockchain systems are much less explored. In this paper, we conduct an empirical study on blockchain's system vulnerabilities from four representative blockchains, Bitcoin, Ethereum, Monero, and Stellar. Specifically, we first design a systematic filtering process to effectively identify 1,037 vulnerabilities and their 2,317 patches from 34,245 issues/PRs (pull requests) and 85,164 commits on GitHub. We thus build the first blockchain vulnerability dataset. We then perform unique analyses of this dataset at three levels, including (i) file-level vulnerable module categorization by identifying and correlating module paths across projects, (ii) text-level vulnerability type clustering by natural language processing and similarity-based sentence clustering, and (iii) code-level vulnerability pattern analysis by generating and clustering code change signatures that capture both syntactic and semantic information of patch code fragments. Our analyses reveal three key findings: (i) some blockchain modules are more susceptible than the others; notably, each of the modules related to consensus, wallet, and networking has over 200 issues; (ii) about 70% of blockchain vulnerabilities are of traditional types, but we also identify four new types specific to blockchains; and (iii) we obtain 21 blockchain-specific vulnerability patterns that capture unique blockchain attributes and statuses, and demonstrate that they can be used to detect similar vulnerabilities in other popular blockchains, such as Dogecoin, Bitcoin SV, and Zcash.

cs.CR

BlockScope: Detecting and Investigating Propagated Vulnerabilities in Forked Blockchain Projects

Due to the open-source nature of the blockchain ecosystem, it is common for new blockchains to fork or partially reuse the code of classic blockchains. For example, the popular Dogecoin, Litecoin, Binance BSC, and Polygon are all variants of Bitcoin/Ethereum. These "forked" blockchains thus could encounter similar vulnerabilities that are propagated from Bitcoin/Ethereum during forking or subsequently commit fetching. In this paper, we conduct a systematic study of detecting and investigating the propagated vulnerabilities in forked blockchain projects. To facilitate this study, we propose BlockScope, a novel tool that can effectively and efficiently detect multiple types of cloned vulnerabilities given an input of existing Bitcoin/Ethereum security patches. Specifically, BlockScope adopts similarity-based code match and designs a new way of calculating code similarity to cover all the syntax-wide variant (i.e., Type-1, Type-2, and Type-3) clones. Moreover, BlockScope automatically extracts and leverages the contexts of patch code to narrow down the search scope and locate only potentially relevant code for comparison. Our evaluation shows that BlockScope achieves good precision and high recall both at 91.8% (1.8 times higher recall than that in ReDeBug). BlockScope allows us to discover 101 previously unknown vulnerabilities in 13 out of the 16 forked projects of Bitcoin and Ethereum, including 16 from Dogecoin, 6 from Litecoin, 1 from Binance, and 4 from Optimism. We have reported all the vulnerabilities to their developers; 40 of them have been patched or accepted, 66 were acknowledged or under pending, and only 4 were rejected. We further investigate the propagation and patching processes of discovered vulnerabilities, and reveal three types of vulnerability propagation from source to forked projects, as well as the long delay (over 200 days) for releasing patches in Bitcoin forks.

cs.CR

Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation

We establish the equivalence between weak and viscosity solutions to the nonhomogeneous double phase equation with lower-order term $$ -{\rm div}(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du)=f(x,u,Du),\quad 1<p\le q<\infty, a(x)\ge0. $$ We find some appropriate hypotheses on the coefficient $a(x)$, the exponents $p, q$ and the nonlinear term $f$ to show that the viscosity solutions with {\em a priori} Lipschitz continuity are weak solutions of such equation by virtue of the $\inf$($\sup$)-convolution techniques. The reverse implication can be concluded through comparison principles. Moreover, we verify that the bounded viscosity solutions are exactly Lipschitz continuous, which is also of independent interest.

math.AP

Harnack inequality for the nonlocal equations with general growth

We consider a class of generalized nonlocal $p$-Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solutions to such nonlocal problems by using the expansion of positivity and energy estimates.

math.AP