Efficient High-Radix GF(p) Montgomery Modular Multiplication Via Deep Use Of Multipliers

Wu, Ruoyu; Xu, Ming; Yang, Yingqing; Tian, Guanzhong; Yu, Ping; Zhao, Yangfan; Lian, Bin; Ma, Longhua

doi:10.1109/tcsii.2022.3197314

Cited by 2 publications

(4 citation statements)

References 19 publications

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“…Ref. [9] outperforms ours by 21% in latency, but we have an advantage of 26% in area and 6% in ATP for a 256-bit modulus. The advantage of our ATP grows as the modulus size increases.…”

Section: Results Comparison and Discussionmentioning

confidence: 66%

“…Ref. [9] introduced a separate iterative MMM that needs pre-computation, making the calculation process more efficient. However, refs.…”

Section: Previous Workmentioning

confidence: 99%

“…However, refs. [9,29,30] did not modify the core iteration steps and needed extra resources with the carry-save adders. Ref.…”

Section: Previous Workmentioning

confidence: 99%

“…Hardware implementations can solve computational burdens and limited memory problems since they perform better and do not occupy the computational resources of a central processor. Some existing works [9][10][11] are dedicated to the efficient hardware implementations of PCS with low areas.…”

Section: Introduction 1research Backgroundmentioning

confidence: 99%

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A Low-Cost High-Performance Montgomery Modular Multiplier Based on Pipeline Interleaving for IoT Devices

Ren

Wang

et al. 2023

Electronics

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Modular multiplication is a crucial operation in public-key cryptography systems such as RSA and ECC. In this study, we analyze and improve the iteration steps of the classic Montgomery modular multiplication (MMM) algorithm and propose an interleaved pipeline (IP) structure, which meets the high-performance and low-cost requirements for Internet of Things devices. Compared to the classic pipeline structure, the IP does not require a multiplexing processing element (PE), which helps shorten the data path of intermediate results. We further introduce a disruption in the critical path to complete an iterative step of the MMM algorithm in two clock cycles. Our proposed hardware architecture is implemented on Xilinx Virtex-7 Series FPGA, using DSP48E1, to realize the multiplier. The implemented results show that the modular multiplication of 1024 bits by 2048 bits requires 1.03 μs and 2.13 μs, respectively. Moreover, our area–time–product analysis reveals a favorable outcome compared to the state-of-the-art designs across a 1024-bit and 2048-bit modulus.

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“…Ref. [9] outperforms ours by 21% in latency, but we have an advantage of 26% in area and 6% in ATP for a 256-bit modulus. The advantage of our ATP grows as the modulus size increases.…”

Section: Results Comparison and Discussionmentioning

confidence: 66%

“…Ref. [9] introduced a separate iterative MMM that needs pre-computation, making the calculation process more efficient. However, refs.…”

Section: Previous Workmentioning

confidence: 99%

“…However, refs. [9,29,30] did not modify the core iteration steps and needed extra resources with the carry-save adders. Ref.…”

Section: Previous Workmentioning

confidence: 99%

Section: Introduction 1research Backgroundmentioning

confidence: 99%

See 2 more Smart Citations

A Low-Cost High-Performance Montgomery Modular Multiplier Based on Pipeline Interleaving for IoT Devices

Ren

Wang

et al. 2023

Electronics

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Verification of Synthesized by the IP-core Generator Multipliers of Extended Galois Fields GF(pⁿ) Elements

Zholubak,

Hlukhov

2023

2023 13th International Conference on Dependable Systems, Services and Technologies (DESSERT)

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Efficient High-Radix GF(p) Montgomery Modular Multiplication Via Deep Use Of Multipliers

Cited by 2 publications

References 19 publications

A Low-Cost High-Performance Montgomery Modular Multiplier Based on Pipeline Interleaving for IoT Devices

A Low-Cost High-Performance Montgomery Modular Multiplier Based on Pipeline Interleaving for IoT Devices

Verification of Synthesized by the IP-core Generator Multipliers of Extended Galois Fields GF(pⁿ) Elements

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Efficient High-Radix GF(p) Montgomery Modular Multiplication Via Deep Use Of Multipliers

Cited by 2 publications

References 19 publications

A Low-Cost High-Performance Montgomery Modular Multiplier Based on Pipeline Interleaving for IoT Devices

A Low-Cost High-Performance Montgomery Modular Multiplier Based on Pipeline Interleaving for IoT Devices

Verification of Synthesized by the IP-core Generator Multipliers of Extended Galois Fields GF(pn) Elements

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Verification of Synthesized by the IP-core Generator Multipliers of Extended Galois Fields GF(pⁿ) Elements