Related papers: On the Quantum Equivalence between $S|LWE\rangle$ …
Although symmetric informationally complete positive operator valued measures (SIC POVMs, or SICs for short) have been constructed in every dimension up to 67, a general existence proof remains elusive. The purpose of this paper is to show…
AI-powered attacks on Learning with Errors (LWE), an important hard math problem in post-quantum cryptography, rival or outperform "classical" attacks on LWE under certain parameter settings. Despite the promise of this approach, a dearth…
Large Language Models (LLMs) are increasingly integrated into daily routines, yet they raise significant privacy and safety concerns. Recent research proposes collaborative inference, which outsources the early-layer inference to ensure…
Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…
In this paper, we investigate the complexity of one-dimensional dynamic programming, or more specifically, of the Least-Weight Subsequence (LWS) problem: Given a sequence of $n$ data items together with weights for every pair of the items,…
O'Hearn's Incorrectness Logic (IL) has sparked renewed interest in static analyses that aim to detect program errors rather than prove their absence, thereby avoiding false alarms -- a critical factor for practical adoption in industrial…
The cryptosystem based on the Learning-with-Errors (LWE) problem is considered as a post-quantum cryptosystem, because it is not based on the factoring problem with large primes which is easily solved by a quantum computer. Moreover, the…
The Ring Learning-With-Errors (RLWE) problem shows great promise for post-quantum cryptography and homomorphic encryption. We describe a new attack on the non-dual search RLWE problem with small error widths, using ring homomorphisms to…
This paper revisits the CHAMPAGNE algorithm within the Sparse Bayesian Learning (SBL) framework and establishes its connection to reweighted sparse coding. We demonstrate that the SBL objective can be reformulated as a reweighted…
Some hard problems from lattices, like LWE (Learning with Errors), are particularly suitable for application in Cryptography due to the possibility of using worst-case to average-case reductions as evidence of strong security properties. In…
We prove the first hardness results against efficient proof search by quantum algorithms. We show that under Learning with Errors (LWE), the standard lattice-based cryptographic assumption, no quantum algorithm can weakly automate…
Large language models (LLMs) have demonstrated remarkable performance, yet their diverse strengths and weaknesses prevent any single LLM from achieving dominance across all tasks. Ensembling multiple LLMs is a promising approach to generate…
Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
The assumed hardness of the Linear Code Equivalence problem (LCE) lies at the core of the security of the LESS signature scheme and other signature schemes with advanced functionalities. The LCE problem asks to determine whether two linear…
Ring Learning With Error (RLWE) algorithm is used in Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE) algorithm. The existing classical crypto algorithms may be broken in quantum computers. The adversaries can store all…
We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples…
Software is prone to security vulnerabilities. Program analysis tools to detect them have limited effectiveness in practice due to their reliance on human labeled specifications. Large language models (or LLMs) have shown impressive code…
Incorrectness Separation Logic (ISL) is a proof system that is tailored specifically to resolve problems of under-approximation in programs that manipulate heaps, and it primarily focuses on bug detection. This approach is different from…
This paper proposes CES, a task to evaluate the abilities of LLMs in simulating program execution and using that reasoning in programming tasks. Besides measuring the correctness of variable predictions during execution simulation, CES…