A High-Performance and Low-Cost Montgomery Modular Multiplication Based on Redundant Binary Representation

Li, Bing; Wang, Jinlei; Ding, Guangfei; Fu, Haisheng; Lei, Bingjie; Yang, Haitao; Bi, Jiangang; Lei, Shaochong

doi:10.1109/tcsii.2021.3053630

Cited by 10 publications

(3 citation statements)

References 18 publications

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“…Ref. [5] uses the RNS-based modular multiplication system to achieve better frequency and ATP, but it avoids the pipeline design like [21]. In this paper, RBR is introduced to lessen the critical path in calculating units.…”

Section: Results and Comparisonsmentioning

confidence: 99%

“…The carry propagation problem in modular multiplication is solved by converting the carry into a redundant number. The proof of Algorithm 1 has been provided by [21]; we only discuss its critical path and area consumption in this paper.…”

Section: Algorithm Fundamentalsmentioning

confidence: 99%

“…In that case, Ref. [21] has proposed a Redundant Binary Representation MMM (RBR-MMM) algorithm to solve the carry-chain problem by bringing the operations of MMM into the redundant system, which successfully eliminates the long carry chain and improves the performance of MMM.…”

Section: Introductionmentioning

confidence: 99%

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A Scalable Montgomery Modular Multiplication Architecture with Low Area-Time Product Based on Redundant Binary Representation

Zhaoji

Zhang

2022

Electronics

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The Montgomery modular multiplication is an integral operation unit in the public key cryptographic algorithm system. Previous work achieved good performance at low input widths by combining Redundant Binary Representation (RBR) with Montgomery modular multiplication, but it is difficult to strike a good balance between area and time as input bit widths increase. To solve this problem, based on the redundant Montgomery modular multiplication, in this paper, we propose a flexible and pipeline hardware implementation of the Montgomery modular multiplication. Our proposed structure guarantees a single-cycle delay between two-stage pipeline units and reduces the length of the critical path by redistributing the data paths between the pipelines and preprocessing the input in the loop. By analyzing the structure and comparing the related work in this paper, our structure ensures a lower area-time product while achieving a controllable and small area consumption. The comprehensive results under different Taiwan Semiconductor Manufacturing Company (TSMC) processes demonstrate the advantages of our structure in terms of flexibility and area-time product.

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Section: Results and Comparisonsmentioning

confidence: 99%

Section: Algorithm Fundamentalsmentioning

confidence: 99%