Securing Sparse Matrix Math in the Cloud
![Homomorphic encryption of sparse matrix-vector multiplication (SpMV) in compressed sparse row (CSR) format introduces substantial computational overhead, as each element-wise product, while achievable, necessitates a costly homomorphic rotation and multiplication for subsequent aggregation-a limitation stemming from the inability to efficiently combine encrypted partial results without incurring these operations on every addition required to construct the final encrypted vector sum [latex] \sum_{j=1}^{n} A_{ij} x_j [/latex].](https://arxiv.org/html/2603.04742v1/2603.04742v1/x1.png)
A new approach to privacy-preserving sparse matrix-vector multiplication unlocks significant performance gains using homomorphic encryption.
![Homomorphic encryption of sparse matrix-vector multiplication (SpMV) in compressed sparse row (CSR) format introduces substantial computational overhead, as each element-wise product, while achievable, necessitates a costly homomorphic rotation and multiplication for subsequent aggregation-a limitation stemming from the inability to efficiently combine encrypted partial results without incurring these operations on every addition required to construct the final encrypted vector sum [latex] \sum_{j=1}^{n} A_{ij} x_j [/latex].](https://arxiv.org/html/2603.04742v1/2603.04742v1/x1.png)
A new approach to privacy-preserving sparse matrix-vector multiplication unlocks significant performance gains using homomorphic encryption.

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A new modification to the Fully Homomorphic Modified Rivest Scheme enhances security while preserving the ability to compute on encrypted data.

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/|\text{Baseline}-\text{Human}|[/latex]- achieved by large language models on the ASAP-SAS dataset; a transformer ensemble (point A, Ormerod, 2022) and a fine-tuned GPT ensemble (point B, Ormerod & Kwako, 2024) progressively surpass earlier baselines-with a subsequent GPT-4 implementation (point C, Jiang & Bosch, 2024) projected to reach a normalized score of -1.52-indicating a substantial, ongoing refinement in automated assessment capabilities.](https://arxiv.org/html/2603.04820v1/2603.04820v1/x1.png)
A comprehensive analysis reveals that current artificial intelligence systems struggle to accurately assess short-answer responses, exposing fundamental limitations in their understanding of meaning.

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Both John Marston and Arthur Morgan star in truly remarkable stories, filled with both emotional depth and exciting adventures set in vast, lively open worlds.