Journal on Communications ›› 2020, Vol. 41 ›› Issue (12): 100-109.doi: 10.11959/j.issn.1000-436X.2020226
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Bin YU, Hai HUANG, Zhiwei LIU, Shilei ZHAO, Ning NA
Revised:2020-09-17
Online:2020-12-25
Published:2020-12-01
Supported by:CLC Number:
Bin YU, Hai HUANG, Zhiwei LIU, Shilei ZHAO, Ning NA. Design and implementation of high-speed scalar multiplier for multi-elliptic curve[J]. Journal on Communications, 2020, 41(12): 100-109.
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| 步骤 | 模乘 | 模加减 |
| 1 | t1←Z1Z1 | — |
| 2 | t2←Y1Y1 | t3←x1+t1, t4←X1-t1 |
| 3 | t1←t3t4 | — |
| 4 | t3←Y1Z1 | t4←8t2 |
| 5 | t5←X1t4 | t1←3t1 |
| 6 | t3←t1t1 | Z3←t3+t3 |
| 7 | t2←t2t4 | X3←t3-t5, t4←1.5t5-t3 |
| 8 | t1←t1t4 | — |
| 9 | — | Y3←t1-t2 |
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| 步骤 | 模乘 | 模加减 |
| 1 | t1←Z1Z1 | — |
| 2 | t2←Z2Z2 | — |
| 3 | X3←X2t1 | — |
| 4 | t3←X1t2 | — |
| 5 | t1←t1Z1 | t6←X3+t3, t4←X3-t3 |
| 6 | t5←t4t4 | — |
| 7 | t2←t2z2 | — |
| 8 | t1←Y2t1 | — |
| 9 | t2←Y1t2 | — |
| 10 | Y3←t5t6 | — |
| 11 | t6←t4t5 | t3←t1-t2, t2←t1+t2 |
| 12 | t1←t3t3 | — |
| 13 | t5←t2t6 | X3←t1-Y3 |
| 14 | Z3←Z1Z2 | t6←Y3-2X3 |
| 15 | Y3←t3t6 | — |
| 16 | Z3←Z3t4 | Y3←Y3-t5 |
| 17 | — | Y3←0.5Y3 |
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| 步骤 | 模乘 | 模加减 |
| 1 | — | t1←X2+Z2 |
| 2 | t6←t1t1 | t2←X2-Z2 |
| 3 | t7←t2t2 | t3←X3-Z3 |
| 4 | t8←t1t3 | t4←X3+Z3, t5←t6-t7 |
| 5 | t9←t2t4 | — |
| 6 | X2←t6t7 | X3←t8+t9,Z3=t8-t9 |
| 7 | X3←X3X3 | — |
| 8 | Z2←121665t5 | — |
| 9 | Z3←Z3Z3 | Z2←Z2+t6 |
| 10 | Z2←Z2t5 | — |
| 11 | Z3←Z3X1 | — |
| 12 | — | Z3约简 |
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| 步骤 | 模乘 | 模加减 |
| 1 | t1←Z1Z1 | — |
| 2 | t2←Y2Z1 | — |
| 3 | t3←X2t1 | — |
| 4 | t1←t1t2 | t2←t3-X1, t3←t3+x1 |
| 5 | t4←t2t2 | t1←t1-Y1 |
| 6 | Z3←Z1t2 | — |
| 7 | t2←t2t4 | — |
| 8 | t3←t3t4 | — |
| 9 | t5←t1t1 | — |
| 10 | t4←X1t4 | X3←t5-t3 |
| 11 | t2←Y1t2 | t3←t4-X3 |
| 12 | t1←t1t3 | — |
| 13 | — | Y3←t1-t2 |
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| 运算 | λG/周期 | λP/周期 | λP+μG/周期 | Curve25519/周期 |
| 预计算 | 0 | 24 | 168 | 0 |
| 迭代（平均） | 1 233 | 3 684 | 3 684 | 3 572 |
| 迭代（最大） | 1 285 | 4 228 | 4 228 | 3 572 |
| 模逆（平均） | 384 | 384 | 384 | 384 |
| 模逆（最大） | 512 | 512 | 512 | 510 |
| 后处理 | 7 | 7 | 7 | 3 |
| 合计（平均） | 1 624 | 4 099 | 4 243 | 3 956 |
| 合计（最大） | 1 804 | 4 771 | 4 915 | 4 082 |
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| 方案 | 曲线 | 工艺/nm | 主频/MHz | 门数/个 | 运算速度/（千次·秒-1） | 单次时间/μs | AT |
| secp256r1(λG) | 384.8 | 2.60 | 2 657 | ||||
| 本文工作 | secp256r1(λP) | 55 | 625.00 | 1 022×103 | 152.5 | 6.56 | 6 704 |
| Curve25519 | 157.9 | 6.33 | 6 469 | ||||
| 文献[4] | secp256r1 | 65 | 549.45 | 447×103 | 1.38 | 0.73 | 326 310 |
| 文献[5] | secp256r1 | 65 | 188.00 | 3.5×106 | 80 | 12.5 | 43 750 |
| 文献[6] | secp256r1 | 90 | 217.00 | 313×103 | 1.71 | 0.76 | 237 880 |
| 文献[7] | secp256r1 | 90 | 185.00 | 540×103 | 8.30 | 120 | 64 800 |
| 文献[25] | secp256r1 | 90 | 256.40 | 82.8×103 | 3.22 | 0.31 | 25 668 |
| 文献[26] | secp256r1 | 130 | 215.00 | 208×103 | 4.76 | 0.21 | 43 680 |
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