High-Performance Pipelined Architecture of Point Multiplication on Koblitz Curves

Li, Canbing; Li, Shuguo

doi:10.1109/tcsii.2017.2785382

Cited by 18 publications

(45 citation statements)

References 17 publications

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“…On Virtex-7, both proposed architectures are state-ofthe-art designs, which perform 93.8% and 71.2% better than the best existing work [12]. On Virtex-5, the performance of 6CC-6CC architecture is 5.5% better than the best existing work [30]. The superiority in performance is evident, not to mention the ability to support more than one field.…”

Section: B the Synthesis Results Of Our Workmentioning

confidence: 85%

“…This means that the results of 6CC-6CC (or 6CC-4CC) architecture on both fields comes from the same implementation, hence have the same maximum frequency and occupied LUTs. For each of the other works that appears in both tables like [18] and [30], the results of GF (2 283 ) and GF (2 571 ) are based on the same architecture, but actually comes from different implementations. Since these different implementations can be optimized according to specific field parameters, the comparison between the proposed architectures and others is actually not fair.…”

Section: Implementation Results and Comparisons A Overviewmentioning

confidence: 99%

“…The superiority in performance is evident, not to mention the ability to support more than one field. The performance of 6CC-4CC architecture on Virtex-5 is far better than [18] and [12], but is 10.4% worse than [30]. However, the high-performance PM architecture in [30] is designed to work only on single preset field over Koblitz curves, which is a special case of Simplified Weierstrass Curves.…”

Section: B the Synthesis Results Of Our Workmentioning

confidence: 99%

“…The performance of 6CC-4CC architecture on Virtex-5 is far better than [18] and [12], but is 10.4% worse than [30]. However, the high-performance PM architecture in [30] is designed to work only on single preset field over Koblitz curves, which is a special case of Simplified Weierstrass Curves. But the proposed 6CC-4CC design is compatible with all Simplified Weierstrass Curves cases, and supports both GF (2 283 ) and GF (2 571 ) fields.…”

Section: B the Synthesis Results Of Our Workmentioning

confidence: 99%

“…Over Koblitz curves, special cases of Weierstrass Curve, Frobenius mappings can be used to accelerate PM [27]- [29]. Recently, Li and Li [30] proposed a high-performance PM architecture by applying pipelined mixed-form double-digit scalar converter with compact recoding over Koblitz curves. Frobenius mappings were applied to get a tremendous promotion in computation time.…”

Section: ) Bit-parallel Multipliermentioning

confidence: 99%

See 4 more Smart Citations

Innovative Dual-Binary-Field Architecture for Point Multiplication of Elliptic Curve Cryptography

Wang

Zhang

et al. 2021

IEEE Access

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High-performance Elliptic Curve Cryptography (ECC) implementation in encryption authentication severs has become a challenge due to the explosive growth of e-commerce's demand for speed and security. Point multiplication (PM) is the most common and complex operation in ECC which directly determines the performance of the whole system. This article proposes a 6CC-6CC (clock cycle) dual-field PM architecture and a 6CC-4CC dual-field PM architecture based on maximizing utilization of Karatsuba multipliers and re-ordering schedule strategy in PM. The Montgomery Ladder algorithm used in PM is modified to a 4CC algorithm for better resource utilization and parallel computation. To solve the frequency drop problem while working on large finite field, the PM architectures for high and low field are carefully studied to have universal critical path length and balanced performance. Both of the architectures are implemented over GF(2 571 ) and GF(2 283 ) on Xilinx Virtex-5 and Virtex-7 FPGAs (Field-Programmable Gate Array) for comparison. The 6CC-6CC architecture is shown to have the best performance on GF(2 571 ), which achieves one PM operation in 17.44 µs using 81549 LUTs (Look-Up-Table ) with the frequency of 197.2 MHz on Virtex-5, and 12.55 µs using 80970 LUTs with the frequency of 274.1 MHz on Virtex-7. The 6CC-4CC architecture performs better on GF(2 283 ) with the shortest computation time. It takes only 3.21 µs to finish one PM operation on Virtex-5 and 2.22 µs on Virtex-7, which are faster than all the previous designs. The implementation results prove that the proposed architectures have state-of-the-art performance as well as higher versatility for ECC designs.INDEX TERMS Elliptic curve cryptography (ECC), dual-field point multiplication, montgomery ladder, field-programmable gate array (FPGA) implementation.

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Section: B the Synthesis Results Of Our Workmentioning

confidence: 85%

Section: Implementation Results and Comparisons A Overviewmentioning

confidence: 99%