Xiao Liang

Boyan Duan, Xiao Liang, Shuai Lu et al.

Automated theorem proving in Euclidean geometry, particularly for International Mathematical Olympiad (IMO) level problems, remains a major challenge and an important research focus in Artificial Intelligence. In this paper, we present a highly efficient method for geometry theorem proving that runs entirely on CPUs without relying on neural network-based inference. Our initial study shows that a simple random strategy for adding auxiliary points can achieve silver-medal level human performance on IMO. Building on this, we propose HAGeo, a Heuristic-based method for adding Auxiliary constructions in Geometric deduction that solves 28 of 30 problems on the IMO-30 benchmark, achieving gold-medal level performance and surpassing AlphaGeometry, a competitive neural network-based approach, by a notable margin. To evaluate our method and existing approaches more comprehensively, we further construct HAGeo-409, a benchmark consisting of 409 geometry problems with human-assessed difficulty levels. Compared with the widely used IMO-30, our benchmark poses greater challenges and provides a more precise evaluation, setting a higher bar for geometry theorem proving.

Chen Chen, Xiao Liang, Bogdan Carbunar et al.

Data privacy is critical in instilling trust and empowering the societal pacts of modern technology-driven democracies. Unfortunately, it is under continuous attack by overreaching or outright oppressive governments, including some of the world's oldest democracies. Increasingly-intrusive anti-encryption laws severely limit the ability of standard encryption to protect privacy. New defense mechanisms are needed. Plausible deniability (PD) is a powerful property, enabling users to hide the existence of sensitive information in a system under direct inspection by adversaries. Popular encrypted storage systems such as TrueCrypt and other research efforts have attempted to also provide plausible deniability. Unfortunately, these efforts have often operated under less well-defined assumptions and adversarial models. Careful analyses often uncover not only high overheads but also outright security compromise. Further, our understanding of adversaries, the underlying storage technologies, as well as the available plausible deniable solutions have evolved dramatically in the past two decades. The main goal of this work is to systematize this knowledge. It aims to: - identify key PD properties, requirements, and approaches; - present a direly-needed unified framework for evaluating security and performance; - explore the challenges arising from the critical interplay between PD and modern system layered stacks; - propose a new "trace-oriented" PD paradigm, able to decouple security guarantees from the underlying systems and thus ensure a higher level of flexibility and security independent of the technology stack. This work is meant also as a trusted guide for system and security practitioners around the major challenges in understanding, designing, and implementing plausible deniability into new or existing systems.

Nai-Hui Chia, Kai-Min Chung, Xiao Liang et al.

From the minimal assumption of post-quantum semi-honest oblivious transfers, we build the first $ε$-simulatable two-party computation (2PC) against quantum polynomial-time (QPT) adversaries that is both constant-round and black-box (for both the construction and security reduction). A recent work by Chia, Chung, Liu, and Yamakawa (FOCS'21) shows that post-quantum 2PC with standard simulation-based security is impossible in constant rounds, unless either $\mathbf{NP} \subseteq \mathbf{BQP}$ or relying on non-black-box simulation. The $ε$-simulatability we target is a relaxation of the standard simulation-based security that allows for an arbitrarily small noticeable simulation error $ε$. Moreover, when quantum communication is allowed, we can further weaken the assumption to post-quantum secure one-way functions (PQ-OWFs), while maintaining the constant-round and black-box property. Our techniques also yield the following set of constant-round and black-box two-party protocols secure against QPT adversaries, only assuming black-box access to PQ-OWFs: - extractable commitments for which the extractor is also an $ε$-simulator; - $ε$-zero-knowledge commit-and-prove whose commit stage is extractable with $ε$-simulation; - $ε$-simulatable coin-flipping; - $ε$-zero-knowledge arguments of knowledge for $\mathbf{NP}$ for which the knowledge extractor is also an $ε$-simulator; - $ε$-zero-knowledge arguments for $\mathbf{QMA}$. At the heart of the above results is a black-box extraction lemma showing how to efficiently extract secrets from QPT adversaries while disturbing their quantum state in a controllable manner, i.e., achieving $ε$-simulatability of the post-extraction state of the adversary.