Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.09767

Faster PMNS Multi-precision Multiplications Using Truncated Montgomery Technique

Laurent-Stéphane Didier·Alexy Dutois-Ruiz·Jean-Marc Robert
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Polynomial Modular Number Systems (PMNS) aim to represent elements of fields or rings of large characteristics using polynomials satisfying bounds on some parameters (degree, absolute values of the coefficients). Those PMNS, while some conditions are fulfilled, using convenient parameters and implementation features, allow some speed-ups in cryptographic computations. Recent works (Meloni \emph{et al.} \cite{MeloniPV25}) propose better speed-ups by improving the parameter generation of the system, and by using multi-precision polynomial coefficients, i.e. coefficients stored using several machine words. In this work, we first present PMNS schoolbook software implementation better in some context than the Toeplitz state-of-the-art counterpart of \cite{MeloniPV25}, taking advantage of smaller memory cost by being free to choose a smaller $n$ parameter, minimizing at the same time the complexity of the multiplication. This implementation for 4096 bit modulo size shows element size smaller by 11\% and 20 \% speed-up. We thus present a new improvement on the PMNS, applying to the \textsl{internal reduction} an approach similar to the truncated Montgomery reduction technique presented by Didier \emph{et al.} in \cite{DidierEGR24}. In the context of software implementations using \texttt{AVX512} instruction set extension, and modulo size up to 8192 bits, this new approach allows speed-ups up to 15\% in modular multiplication computation, in comparison with conventional approaches.

Explore related subjects

cs.CR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Laurent-Stéphane Didier, Alexy Dutois-Ruiz, Jean-Marc Robert. 2026-10-07. Faster PMNS Multi-precision Multiplications Using Truncated Montgomery Technique. https://arxiv.org/abs/2610.09767

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Matrix Subcode Equivalence problem and its application to signature with MPC-in-the-Head

Nowadays, equivalence problems are widely used in cryptography, most notably to establish cryptosystems such as digital signatures, with MEDS, LESS, PERK as the most recent ones. However, in the context of matrix codes, only the code equivalence problem has been studied, while the subcode equivalence is well-defined in the Hamming metric. In this work, we introduce two new problems: the Matrix Subcode Equivalence Problem and the Matrix Code Permuted Kernel Problem, to which we apply the MPCitH paradigm to build a signature scheme. These new problems, closely related to the Matrix Code Equivalence problem, ask to find an isometry given a code $C$ and a subcode $D$. Furthermore, we prove that the Matrix Subcode Equivalence problem reduces to the Hamming Subcode Equivalence problem, which is known to be NP-Complete, thus introducing the matrix code version of the Permuted Kernel Problem. We also adapt the combinatorial and algebraic algorithms for the Matrix Code Equivalence problem to the subcode case, and we analyze their complexities. We find with this analysis that the algorithms perform much worse than in the code equivalence case, which is the same as what happens in the Hamming metric. Finally, our analysis of the attacks allows us to take parameters much smaller than in the Matrix Code Equivalence case. Coupled with the effectiveness of \textit{Threshold-Computation-in-the-Head} or \textit{VOLE-in-the-Head}, we obtain a signature size of $\approx$ 4 800 Bytes, with a public key of $\approx$ 275 Bytes. We thus obtain a reasonable signature size, which brings diversity in the landscape of post-quantum signature schemes, by relying on a new hard problem. In particular, this new signature scheme performs better than SPHINCS+, with a smaller size of public key + signature. Our signature compares also well with other signature schemes: compared to MEDS, the signature is smaller, and we reduced the size of the sum of signature and public key by a factor close to 5. We also obtain a signature size that is almost half the size of the CROSS signature scheme.

cs.CR↗
arXiv2026

Rethinking Latency Denial-of-Service: Attacking the LLM Serving Framework, Not the Model

LLM inference is inherently expensive, even a modest slowdown can translate into substantial operating costs and severe availability risks. Recently, a growing body of research known as latency attacks focuses on crafting inputs to trigger worst-case output lengths. However, we report a contrary finding that these algorithmic-level latency attacks are largely ineffective against modern LLM serving systems. We reveal that system-level optimization such as continuous batching provides a logical isolation to mitigate contagious latency impact on co-located users. Thus, in this paper, we shift our focus from the algorithm to the system layer, and introduce a new Fill and Squeeze attack strategy targeting the state transition of the scheduler. ``Fill'' first exhausts the global KV cache to induce Head-of-Line blocking, while ``Squeeze'' forces the system into repetitive preemption. By manipulating output lengths using different attack prompts, and leveraging side-channel probing of memory status, we demonstrate that the attack can succeed in a practical black-box setting with much less cost. Extensive evaluations on vLLM indicate up to $75-742\times$ TTFT degradation relative to benign baselines and $1.5-4\times$ average slowdown on Time Per Output Token compared to existing attacks with 30-40% lower attack cost. Code: https://github.com/Phil-Fan/FS-attack

cs.CR↗
arXiv2026

mAVE: A Watermark for Joint Audio-Visual Generation Models

Watermarking joint audio-visual generation supports vendor copyright protection and content provenance. However, independently valid audio and video watermarks do not establish a shared generation session. An adversary can splice watermarked modalities from different sessions, causing the pair to be mistaken for the vendor's original joint output. We introduce mAVE (Manifold Audio-Visual Entanglement), a training-free watermarking framework that strengthens vendor attribution through session binding in native joint audio-visual diffusion transformers. mAVE separates public record retrieval from secret session authentication: a fixed public index locates the server record, while a randomized payload binds audio bits to a session-keyed video grid through a cryptographic digest. One prompt-conditioned joint inversion supports provider-assisted verification of both modalities against a session record, without modifying generator weights or training auxiliary watermark networks. Our analysis establishes implementation-matched distribution preservation and a full-initialization routing/clipping budget, alongside adaptive session-pool security and stable local-perturbation bounds. Experiments on LTX-2 and MOVA show comparable generation quality. mAVE achieves 99.8\% true-positive rate and 0\% observed false-positive rate in the evaluated swap test, and retains 99.2\% true-positive rate under FrameAvg temporal averaging. Same-prompt and similarity-selected swaps further test session authentication beyond perceptual compatibility.

cs.CR↗