arXiv subjects

Guorui Xu

Publications and source records attributed to Guorui Xu.

3 recordsLinked to original sources

arXiv2026

Two-flag degenerations and real circles tangent to three conics

Three general plane conics admit $184$ complex tangent circles, and it had been conjectured that at most $136$ of them could be real. We construct an explicit strongly general triple of smooth conics over $\mathbb{Q}$ with exactly $160$ real tangent circles; the same count therefore occurs on a nonempty Euclidean chamber. The construction combines a fourfold splitting theorem for two flagged double-line degenerations with exact Sturm--Tarski, elimination, and interval certificates. We also show that the Grothendieck--Witt-valued count is $92\mathbb{H}$ and express its real local signs, up to a fixed orientation convention, in terms of curvature differences, residual intersection divisors, and contact normals. The exact-arithmetic code and certificate data are archived in the accompanying repository.

math.AG↗

arXiv2026

A Fan Algorithm for Chow-Witt Rings of Smooth Projective Toric Varieties

Let $R$ be a real closed field and let $X_Σ$ be a smooth projective split toric variety. For an explicitly chosen basis rigidification $\mathfrak r$ of its Picard grading, we prove that the pair $(Σ,\mathfrak r)$ determines the resulting total Chow--Witt ring and give a terminating finite algorithm for all groups, products, twists, and forgetful maps. The ring is identified with an explicit fibre product of the Picard-graded diagonal $\mathbf{I}$-cohomology ring and the integral inverse images of twisted Bockstein kernels over the mod-$2$ Chow ring. Using real cycle classes, we identify the first factor with the cohomology of the real toric variety with all sign local systems. We construct the mod-$2$ cycle map on invariant divisors as explicit deck-transition cocycles and obtain finite signed boundary and product matrices directly from the fan.

math.AG↗

arXiv2020

Towards Efficiently Establishing Mutual Distrust Between Host Application and Enclave for SGX

Since its debut, SGX has been used in many applications, e.g., secure data processing. However, previous systems usually assume a trusted enclave and ignore the security issues caused by an untrusted enclave. For instance, a vulnerable (or even malicious) third-party enclave can be exploited to attack the host application and the rest of the system. In this paper, we propose an efficient mechanism to confine an untrusted enclave's behaviors. The threats of an untrusted enclave come from the enclave-host asymmetries. They can be abused to access arbitrary memory regions of its host application, jump to any code location after leaving the enclave and forge the stack register to manipulate the saved context. Our solution breaks such asymmetries and establishes mutual distrust between the host application and the enclave. It leverages Intel MPK for efficient memory isolation and the x86 single-step debugging mechanism to capture the event when an enclave is existing. It then performs the integrity check for the jump target and the stack pointer. We have solved two practical challenges and implemented a prototype system. The evaluation with multiple micro-benchmarks and representative real-world applications demonstrated the efficiency of our system, with less than 4% performance overhead.

cs.CR↗