arXiv subjects

Yijia Fang

Publications and source records attributed to Yijia Fang.

7 recordsLinked to original sources

arXiv2026

OrionLink: Single Sign-On with Oblivious Identity Brokers

Single Sign-On (SSO) is a federated authentication mechanism that improves user experience by enabling access to multiple services, or Relying Parties (RPs), through a single authentication at an Identity Provider (IdP). To reduce integration complexity, many RPs rely on third-party Identity Brokers (Brokers) that aggregate numerous IdPs into a unified interface, thereby simplifying protocol management and interoperability. However, while brokers ease development, they introduce a fundamental security and privacy risk: sensitive authentication credentials and user behavioral data are exposed to the broker, creating a high-value single point of failure. Existing SSO solutions provide limited protection against these risks. With the goal of achieving broker obliviousness, we address these challenges at their root and present OrionLink, a comprehensive privacy-enhancing SSO pipeline that is compatible with existing brokered SSO architectures and systematically mitigates broker-induced risks without sacrificing usability. OrionLink incorporates two core components: (a) an anonymous pseudonym derivation scheme that generates unlinkable, per-RP identifiers to prevent cross-service user tracking; (b) an anonymous key exchange protocol that establishes end-to-end encrypted channels to protect user data from broker visibility. We further instantiate OrionLink with two new features, preserving broker functionality and deployability. We implemented a prototype of OrionLink within a brokered SSO environment, and experimental evaluation shows that the framework achieves substantial security and privacy improvements with acceptable performance overhead.

cs.CR↗

arXiv2026

Average pairwise Hamming distance of a subset in a hypercube

In this note, we prove that for a subset $\mathcal{F}$ of $\{0,1\}^n$ of density $\frac{1}{8}$, its average pairwise Hamming distance is at least $\frac{n-3}{2}$, with equality attained only by $(n-3)$-dimensional subcubes. This answers a question of Lei Yu, and solves an important open case of a more general question posed by Ahlswede and Katona in 1977.

math.CO↗

arXiv2026

KBF: Knowledge Boundary as Fingerprint for Language Model and Black-Box API Auditing

Relay and reseller APIs mediate access to large language models (LLMs), but users cannot directly verify which model serves them. We introduce \name, a black-box auditing protocol based on stable factual recall near the knowledge boundary, including repeatable wrong answers. KBF generates benign, renewable probes and calibrates audit decisions against reference self-variation. Across 16 production endpoints, KBF detects all 155 economically relevant substitutions without rejecting any of the 16 same-reference controls. KBF remains robust to deployment variation and reaches 95\% TPR at a substitution rate as low as 15\% in mixed-routing simulations. Field audits flag 7 of 28 endpoints across six platforms as statistically inconsistent with their references. After reference enrollment, even GPT-6 Astra costs only approximately \$0.67 per online audit at the recorded API prices.

cs.CR↗

arXiv2026

On cancellative pairs of families of subsets

A pair $(\mathcal{A}, \mathcal{B})$ of families of subsets of $[n]$ is cancellative if whenever $A, A' \in \mathcal{A}, B \in \mathcal{B}$ satisfy $A \cup B=A' \cup B$, then $A=A'$, and whenever $A \in \mathcal{A}, B, B' \in \mathcal{B}$ satisfy $A \cup B=A \cup B'$, then $B=B'$. We show that for every cancellative pair $(\mathcal{A}, \mathcal{B})$, the inequality $|\mathcal{A}||\mathcal{B}| \le 2.25^n$ holds, matching Tolhuizen's $(2.25-o(1))^n$ lower bound construction.

math.CO↗

arXiv2026

VC-Dimension vs Degree: An uncertainty principle for Boolean functions

We prove a support--shattering uncertainty principle for functions on the Boolean cube. Let $\mathbb{F}$ be any field and let $f:\{0,1\}^n\to\mathbb{F}$ be nonzero. If $x^S$ is a maximum-degree monomial in the multilinear representation of $f$, then $\mathrm{supp}(f)$ shatters $S^c$. Consequently, \[ \mathrm{VC}(\mathrm{supp}(f))+\mathrm{deg}_{\mathbb{F}}(f)\ge n . \] For Boolean-valued functions this yields both the real-degree and algebraic-degree forms of the inequality. We derive several consequences. The real Fourier support of a nonzero Boolean function satisfies \[ \mathrm{VC}(\mathrm{Spec}(f))\ge \mathrm{deg}_{\mathbb{F}_2}(f), \qquad \mathrm{VC}(\mathrm{supp}(f))+\mathrm{VC}(\mathrm{Spec}(f))\ge n . \] The same principle gives a low-degree-obstruction proof of the Sauer--Shelah lemma and a product-space analogue based on the Efron--Stein decomposition, recovering the Karpovsky--Milman multivalued Sauer lemma. We also obtain polynomial-method applications, including an arbitrary-field Sziklai--Weiner lower bound and a shattering theorem for null designs, and discuss sharpness and equality examples.

math.CO↗

arXiv2026

Maximizing directed cycles in tournaments

Determining the combinatorial structures that maximize the number of prescribed substructures is a central theme in extremal combinatorics. Grzesik, Král', Lovász and Volec showed that when $\ell$ is not divisible by $4$, the random tournament contains asymptotically the most directed cycles of length $\ell$ among all $n$-vertex tournaments. In the paper, we resolve the remaining cases where $\ell$ is divisible by $4$. We show that, in this regime, the so-called carousel tournament asymptotically maximizes the number of directed $\ell$-cycles among all $n$-vertex tournaments, and in particular contains strictly more such cycles than the random tournament. This confirms the conjecture of Bartley and Day.

math.CO↗

arXiv2025

Canonical Ramsey: triangles, rectangles and beyond

In a seminal work, Cheng and Xu showed that if $S$ is a square or a triangle with a certain property, then for every positive integer $r$ there exists $n_0(S)$ independent of $r$ such that every $r$-coloring of $\mathbb{E}^n$ with $n\ge n_0(S)$ contains a monochromatic or a rainbow congruent copy of $S$. Gehér, Sagdeev, and Tóth formalized this dimension independence as the canonical Ramsey property and proved it for all hypercubes, thereby covering rectangles whose squared aspect ratio $(a/b)^2$ is rational. They asked whether this property holds for all triangles and for all rectangles. (1) We resolve both questions. More precisely, for triangles we confirm the property in $\mathbb{E}^4$ by developing a novel rotation-sphereical chaining argument. For rectangles, we introduce a structural reduction to product configurations of bounded color complexity, enabling the use of the simplex Ramsey theorem together with product Ramsey theorem. (2) Beyond this, we develop a concise perturbation framework based on an iterative embedding coupled with the Frankl-Rödl simplex super-Ramsey theorem, which yields the canonical Ramsey property for a natural class of 3-dimensional simplices and also furnishes an alternative proof for triangles.

math.CO↗