ALLMod: Exploring Area-Efficiency of LUT-based Large Number Modular Reduction via Hybrid Workloads
Modular arithmetic, particularly modular reduction, is widely used in cryptographic applications such as homomorphic encryption (HE) and zero-knowledge proofs (ZKP). High-bit-width operations are crucial for enhancing security; however, they are computationally intensive due to the large number of m...
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| Vydáno v: | 2025 62nd ACM/IEEE Design Automation Conference (DAC) s. 1 - 7 |
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IEEE
22.06.2025
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| Abstract | Modular arithmetic, particularly modular reduction, is widely used in cryptographic applications such as homomorphic encryption (HE) and zero-knowledge proofs (ZKP). High-bit-width operations are crucial for enhancing security; however, they are computationally intensive due to the large number of modular operations required. The lookup-table-based (LUT-based) approach, a "space-for-time" technique, reduces computational load by segmenting the input number into smaller bit groups, pre-computing modular reduction results for each segment, and storing these results in LUTs. While effective, this method incurs significant hardware overhead due to extensive LUT usage. In this paper, we introduce ALLMod, a novel approach that improves the area efficiency of LUT-based largenumber modular reduction by employing hybrid workloads. Inspired by the iterative method, ALLMod splits the bit groups into two distinct workloads, achieving lower area costs without compromising throughput. We first develop a template to facilitate workload splitting and ensure balanced distribution. Then, we conduct design space exploration to evaluate the optimal timing for fusing workload results, enabling us to identify the most efficient design under specific constraints. Extensive evaluations show that ALLMod achieves up to \lt sup\gt1\lt/sup\gt|.65 \times and 3 \times improvements in area efficiency over conventional LUT-based methods for bit-widths of 128 and 8,192, respectively. |
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| AbstractList | Modular arithmetic, particularly modular reduction, is widely used in cryptographic applications such as homomorphic encryption (HE) and zero-knowledge proofs (ZKP). High-bit-width operations are crucial for enhancing security; however, they are computationally intensive due to the large number of modular operations required. The lookup-table-based (LUT-based) approach, a "space-for-time" technique, reduces computational load by segmenting the input number into smaller bit groups, pre-computing modular reduction results for each segment, and storing these results in LUTs. While effective, this method incurs significant hardware overhead due to extensive LUT usage. In this paper, we introduce ALLMod, a novel approach that improves the area efficiency of LUT-based largenumber modular reduction by employing hybrid workloads. Inspired by the iterative method, ALLMod splits the bit groups into two distinct workloads, achieving lower area costs without compromising throughput. We first develop a template to facilitate workload splitting and ensure balanced distribution. Then, we conduct design space exploration to evaluate the optimal timing for fusing workload results, enabling us to identify the most efficient design under specific constraints. Extensive evaluations show that ALLMod achieves up to \lt sup\gt1\lt/sup\gt|.65 \times and 3 \times improvements in area efficiency over conventional LUT-based methods for bit-widths of 128 and 8,192, respectively. |
| Author | Yan, Shoumeng Liu, Fangxin Guan, Haibing Zhang, Bo Jiang, Li Zhang, Mingzhe Wang, Zongwu Li, Haomin |
| Author_xml | – sequence: 1 givenname: Fangxin surname: Liu fullname: Liu, Fangxin email: liufangxin@sjtu.edu.cn organization: Shanghai Jiao Tong University – sequence: 2 givenname: Haomin surname: Li fullname: Li, Haomin email: haominli@sjtu.edu.cn organization: Shanghai Jiao Tong University – sequence: 3 givenname: Zongwu surname: Wang fullname: Wang, Zongwu organization: Shanghai Jiao Tong University – sequence: 4 givenname: Bo surname: Zhang fullname: Zhang, Bo organization: Ant Group – sequence: 5 givenname: Mingzhe surname: Zhang fullname: Zhang, Mingzhe organization: Ant Group – sequence: 6 givenname: Shoumeng surname: Yan fullname: Yan, Shoumeng organization: Ant Group – sequence: 7 givenname: Li surname: Jiang fullname: Jiang, Li email: ljiang_cs@sjtu.edu.cn organization: Shanghai Jiao Tong University – sequence: 8 givenname: Haibing surname: Guan fullname: Guan, Haibing organization: Shanghai Jiao Tong University |
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| Snippet | Modular arithmetic, particularly modular reduction, is widely used in cryptographic applications such as homomorphic encryption (HE) and zero-knowledge proofs... |
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| SubjectTerms | Cryptography Design automation Hardware Homomorphic encryption Iterative methods Remote working Space exploration Table lookup Throughput Timing |
| Title | ALLMod: Exploring Area-Efficiency of LUT-based Large Number Modular Reduction via Hybrid Workloads |
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