{"ID":2873883,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05552","arxiv_id":"2509.05552","title":"Secure and Efficient $L^p$-Norm Computation for Two-Party Learning Applications","abstract":"Secure norm computation is becoming increasingly important in many real-world learning applications. However, existing cryptographic systems often lack a general framework for securely computing the $L^p$-norm over private inputs held by different parties. These systems often treat secure norm computation as a black-box process, neglecting to design tailored cryptographic protocols that optimize performance. Moreover, they predominantly focus on the $L^2$-norm, paying little attention to other popular $L^p$-norms, such as $L^1$ and $L^\\infty$, which are commonly used in practice, such as machine learning tasks and location-based services. To our best knowledge, we propose the first comprehensive framework for secure two-party $L^p$-norm computations ($L^1$, $L^2$, and $L^\\infty$), denoted as \\mbox{Crypto-$L^p$}, designed to be versatile across various applications. We have designed, implemented, and thoroughly evaluated our framework across a wide range of benchmarking applications, state-of-the-art (SOTA) cryptographic protocols, and real-world datasets to validate its effectiveness and practical applicability. In summary, \\mbox{Crypto-$L^p$} outperforms prior works on secure $L^p$-norm computation, achieving $82\\times$, $271\\times$, and $42\\times$ improvements in runtime while reducing communication overhead by $36\\times$, $4\\times$, and $21\\times$ for $p=1$, $2$, and $\\infty$, respectively. Furthermore, we take the first step in adapting our Crypto-$L^p$ framework for secure machine learning inference, reducing communication costs by $3\\times$ compared to SOTA systems while maintaining comparable runtime and accuracy.","short_abstract":"Secure norm computation is becoming increasingly important in many real-world learning applications. However, existing cryptographic systems often lack a general framework for securely computing the $L^p$-norm over private inputs held by different parties. These systems often treat secure norm computation as a black-bo...","url_abs":"https://arxiv.org/abs/2509.05552","url_pdf":"https://arxiv.org/pdf/2509.05552v1","authors":"[\"Ali Arastehfard\",\"Weiran Liu\",\"Joshua Lee\",\"Bingyu Liu\",\"Xuegang Ban\",\"Yuan Hong\"]","published":"2025-09-06T00:44:20Z","proceeding":"cs.CR","tasks":"[\"cs.CR\"]","methods":"[]","has_code":false}