CAT and DOG: Improved Codes for Private Distributed Matrix Multiplication
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909711857614848 |
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| author | Hofmeister, Christoph Bitar, Rawad Wachter-Zeh, Antonia |
| author_facet | Hofmeister, Christoph Bitar, Rawad Wachter-Zeh, Antonia |
| contents | We present novel constructions of polynomial codes for private distributed matrix multiplication (PDMM/SDMM) using outer product partitioning (OPP). We extend the degree table framework from the literature to cyclic-addition degree tables (CATs). By using roots of unity as evaluation points, we enable modulo-addition in the table. Based on CATs, we present an explicit construction, called CATx, that requires fewer workers than existing schemes in the low-privacy regime. Additionally, we present new families of schemes based on conventional degree tables, called GASPrs and DOGrs, that outperform the state-of-the-art for a wide range of parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CAT and DOG: Improved Codes for Private Distributed Matrix Multiplication Hofmeister, Christoph Bitar, Rawad Wachter-Zeh, Antonia Information Theory We present novel constructions of polynomial codes for private distributed matrix multiplication (PDMM/SDMM) using outer product partitioning (OPP). We extend the degree table framework from the literature to cyclic-addition degree tables (CATs). By using roots of unity as evaluation points, we enable modulo-addition in the table. Based on CATs, we present an explicit construction, called CATx, that requires fewer workers than existing schemes in the low-privacy regime. Additionally, we present new families of schemes based on conventional degree tables, called GASPrs and DOGrs, that outperform the state-of-the-art for a wide range of parameters. |
| title | CAT and DOG: Improved Codes for Private Distributed Matrix Multiplication |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.12371 |