Efficient Large-Width Montgomery Modular Multiplier Design Based on Toom–Cook-5

Toom–Cook-n multiplication is an efficient large-width multiplication algorithm based on a divide-and-conquer strategy, widely used in modular multiplication operations for cryptographic algorithms. Theoretically, as the degree n increases, Toom–Cook-n can split the multiplicands into more sub-terms...

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Bibliographic Details
Published in:Electronics (Basel) Vol. 14; no. 7; p. 1402
Main Authors: Liu, Kuanhao, Wang, Xiaohua, Hao, Yue, Zhang, Jingqi, Wang, Weijiang
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.04.2025
Subjects:
Algorithms
Design
Efficiency
Hardware
Interpolation
Multipliers
Optimization
Performance enhancement
China
Germany
ISSN:2079-9292, 2079-9292
Online Access:Get full text
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Summary:Toom–Cook-n multiplication is an efficient large-width multiplication algorithm based on a divide-and-conquer strategy, widely used in modular multiplication operations for cryptographic algorithms. Theoretically, as the degree n increases, Toom–Cook-n can split the multiplicands into more sub-terms to further enhance the performance of the multiplier. However, constrained by the computational burden brought by the growing size of the interpolation matrix as the degree increases, current research predominantly focuses on Toom–Cook-4 and Toom–Cook-3. This paper proposes a Montgomery modular multiplication design based on Toom–Cook-5, which alleviates the computational difficulty of the interpolation step by introducing an interpolation matrix pre-simplification strategy. Additionally, the design incorporates and optimizes carry–save adder and Karatsuba multiplication, enabling Toom–Cook-5 multiplication to be applied in practical and efficient hardware implementation. This paper presents the ASIC implementation results of the hardware architecture under a 90nm process, demonstrating superior performance compared to previous works.
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ISSN:2079-9292
2079-9292
DOI:10.3390/electronics14071402