Publikation
Depth Optimization of Binary Field GF(2m) Multipliers using MAGIC-Based In-Memory Computing
Saeideh Nabipour; Kamalika Datta; Abhoy Kole; Saeideh Shirinzadeh; Rolf Drechsler
In: Cross-disciplinary Conference on Memory-Centric Computing (CCMCC 2026). IEEE Cross-disciplinary Conference on Memory-Centric Computing (CCMCC-2026), October 28-30, Lyon, France, IEEE, 2026.
Zusammenfassung
Binary field GF(2 m) multiplication is a key operation in cryptographic and error-correcting applications, including elliptic-curve cryptography, coding theory, and selected post-quantum schemes. Memristor-Aided Logic (MAGIC) enables computation directly within memristive crossbars, potentially reducing data-movement overhead while introducing execution
constraints due to logic dependencies and resource limitations. This paper presents an automated framework for implementing
GF(2 m) multipliers on MAGIC-based In-Memory Computing (IMC) architectures. To reduce arithmetic dependency depth, a Reduction-Aware (RA) recursive Karatsuba formulation is proposed that integrates recombination and modular reduction into a unified accumulation network while exploiting XOR sharing and balanced XOR realization. Furthermore, a Dependency-Aware Cell Reuse (DACR) mapping strategy improves logical crossbar utilization through reclamation and reuse of intermediate cells.
The framework integrates arithmetic generation, logic synthesis, and MAGIC-based mapping, and is evaluated for field sizes ranging from GF(2
16) to GF(2 1024). Experimental results generally show substantial reductions in logical execution cycles and allocated memristor count compared with Schoolbook multiplication, particularly for larger fields. These results highlight arithmetic dependency-depth reduction as a key optimization objective for large-field GF(2 m) multipliers under the adopted MAGIC mapping model.