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Keewoo Lee

Publications and source records attributed to Keewoo Lee.

7 recordsLinked to original sources
arXiv2026

Lean-GAP: A Dataset of Formalized Graduate Algebra Problems

We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pipeline consisting of PDF-to-LaTeX preprocessing, autoformalization into Lean 4, and verification of informal-formal correspondence. While the preprocessing and autoformalization stages can be largely automated, we find that verification remains the most subtle and labor-intensive component, requiring careful human oversight. Our contributions include (i) the construction of a structured dataset of formalized exercises, (ii) a systematic methodology for formalizing textbook mathematics, and (iii) an analysis of recurring challenges in the formalization process. We also compare the performance of different autoformalization models and highlight key bottlenecks in translating informal statements into formal language.

cs.LO↗
arXiv2025

Leveraging FPGAs for Homomorphic Matrix-Vector Multiplication in Oblivious Message Retrieval

While end-to-end encryption protects the content of messages, it does not secure metadata, which exposes sender and receiver information through traffic analysis. A plausible approach to protecting this metadata is to have senders post encrypted messages on a public bulletin board and receivers scan it for relevant messages. Oblivious message retrieval (OMR) leverages homomorphic encryption (HE) to improve user experience in this solution by delegating the scan to a resource-rich server while preserving privacy. A key process in OMR is the homomorphic detection of pertinent messages for the receiver from the bulletin board. It relies on a specialized matrix-vector multiplication algorithm, which involves extensive multiplications between ciphertext vectors and plaintext matrices, as well as homomorphic rotations. The computationally intensive nature of this process limits the practicality of OMR. To address this challenge, this paper proposes a hardware architecture to accelerate the matrix-vector multiplication algorithm. The building homomorphic operators in this algorithm are implemented using high-level synthesis, with design parameters for different parallelism levels. These operators are then deployed on a field-programmable gate array platform using an efficient design space exploration strategy to accelerate homomorphic matrix-vector multiplication. Compared to a software implementation, the proposed hardware accelerator achieves a 13.86x speedup.

cs.CR↗
arXiv2025

Bypassing Prompt Guards in Production with Controlled-Release Prompting

Ball et al. recently established that prompt filtering for AI alignment faces a fundamental barrier: under standard cryptographic assumptions, no filter running significantly faster than the protected model can universally distinguish adversarial prompts from benign ones. We investigate whether this impossibility result translates to real-world vulnerabilities in deployed large language model (LLM) systems. We answer affirmatively by introducing controlled-release prompting, a practical instantiation of the theoretical framework that exploits the resource asymmetry between lightweight input filters and the main models they protect. Unlike the theoretical construction, our attack does not require model modification: it generates malicious prompts that are indecipherable by any bounded filter yet remain tractable to the target LLM. We find our attack to be successful on four major chat platforms (Google Gemini, DeepSeek Chat, xAI Grok, and Mistral Le Chat) where baseline methods fail. Additionally, we apply our attack to extract copyrighted data from Gemini. Finally, we provide a systematic evaluation of 14 open-weight prompt guard models, revealing that even reasoning-capable filters cannot reliably detect our attack without incurring prohibitive resource overhead.

cs.LG↗
arXiv2024

SIMD-Aware Homomorphic Compression and Application to Private Database Query

In a private database query scheme (PDQ), a server maintains a database, and users send queries to retrieve records of interest from the server while keeping their queries private. A crucial step in PDQ protocols based on homomorphic encryption is homomorphic compression, which compresses encrypted sparse vectors consisting of query results. In this work, we propose a new homomorphic compression scheme with PDQ as its main application. Unlike existing approaches, our scheme (i) can be efficiently implemented by fully exploiting homomorphic SIMD technique and (ii) enjoys both asymptotically optimal compression rate and asymptotically good decompression complexity. Experimental results show that our approach is 4.7x to 33.2x faster than the previous best results.

cs.CR↗
arXiv2021

On the Scaled Inverse of $(x^i-x^j)$ modulo Cyclotomic Polynomial of the form $Φ_{p^s}(x)$ or $Φ_{p^s q^t}(x)$

The scaled inverse of a nonzero element $a(x)\in \mathbb{Z}[x]/f(x)$, where $f(x)$ is an irreducible polynomial over $\mathbb{Z}$, is the element $b(x)\in \mathbb{Z}[x]/f(x)$ such that $a(x)b(x)=c \pmod{f(x)}$ for the smallest possible positive integer scale $c$. In this paper, we investigate the scaled inverse of $(x^i-x^j)$ modulo cyclotomic polynomial of the form $Φ_{p^s}(x)$ or $Φ_{p^s q^t}(x)$, where $p, q$ are primes with $p<q$ and $s, t$ are positive integers. Our main results are that the coefficient size of the scaled inverse of $(x^i-x^j)$ is bounded by $p-1$ with the scale $p$ modulo $Φ_{p^s}(x)$, and is bounded by $q-1$ with the scale not greater than $q$ modulo $Φ_{p^s q^t}(x)$. Previously, the analogous result on cyclotomic polynomials of the form $Φ_{2^n}(x)$ gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of $\{x^k\}_{k\in\mathbb{Z}}$ in $\mathbb{Z}[x]/Φ_{pq}(x)$ which might be of independent interest.

math.NT↗
arXiv2020

HEAAN Demystified: Accelerating Fully Homomorphic Encryption Through Architecture-centric Analysis and Optimization

Homomorphic Encryption (HE) draws a significant attention as a privacy-preserving way for cloud computing because it allows computation on encrypted messages called ciphertexts. Among numerous HE schemes proposed, HE for Arithmetic of Approximate Numbers (HEAAN) is rapidly gaining popularity across a wide range of applications because it supports messages that can tolerate approximate computation with no limit on the number of arithmetic operations applicable to the corresponding ciphertexts. A critical shortcoming of HE is the high computation complexity of ciphertext arithmetic; especially, HE multiplication (HE Mul) is more than 10,000 times slower than the corresponding multiplication between unencrypted messages. This leads to a large body of HE acceleration studies, including ones exploiting FPGAs; however, those did not conduct a rigorous analysis of computational complexity and data access patterns of HE Mul. Moreover, the proposals mostly focused on designs with small parameter sizes, making it difficult to accurately estimate their performance in conducting a series of complex arithmetic operations. In this paper, we first describe how HE Mul of HEAAN is performed in a manner friendly to computer architects. Then we conduct a disciplined analysis on its computational and memory access characteristics, through which we (1) extract parallelism in the key functions composing HE Mul and (2) demonstrate how to effectively map the parallelism to the popular parallel processing platforms, multicore CPUs and GPUs, by applying a series of optimization techniques such as transposing matrices and pinning data to threads. This leads to the performance improvement of HE Mul on a CPU and a GPU by 42.9x and 134.1x, respectively, over the single-thread reference HEAAN running on a CPU. The conducted analysis and optimization would set a new foundation for future HE acceleration research.

cs.DC↗