LIU Zhiwei, ZHANG Qi, HUANG Hai, YANG Xiaoqiu, CHEN Guanbai, ZHAO Shilei, YU Bin. Design of High Area Efficiency Elliptic Curve Scalar Multiplier Based on Fast Modulo Reduction of Bit Reorganization[J]. Journal of Electronics & Information Technology, 2024, 46(1): 344-352. doi: 10.11999/JEIT221446
Citation:
ZHAO Li, HE Huanjie, MENG Xiangyan, WANG Ning. Research on OFDM-IM Visible Light Communication System Based on Combination Index and Euclidean Distance[J]. Journal of Electronics & Information Technology, 2022, 44(8): 2710-2716. doi: 10.11999/JEIT220112
LIU Zhiwei, ZHANG Qi, HUANG Hai, YANG Xiaoqiu, CHEN Guanbai, ZHAO Shilei, YU Bin. Design of High Area Efficiency Elliptic Curve Scalar Multiplier Based on Fast Modulo Reduction of Bit Reorganization[J]. Journal of Electronics & Information Technology, 2024, 46(1): 344-352. doi: 10.11999/JEIT221446
Citation:
ZHAO Li, HE Huanjie, MENG Xiangyan, WANG Ning. Research on OFDM-IM Visible Light Communication System Based on Combination Index and Euclidean Distance[J]. Journal of Electronics & Information Technology, 2022, 44(8): 2710-2716. doi: 10.11999/JEIT220112
School of Electronics and Information Engineering, Xi’an Technological University, Xi’an 710021, China
Funds:
The National Natural Science Foundation of China (12004292), The General Project of Science and Technology Department of Shaanxi Province – Industry (2022GY-072), Xi’an Science and Technology Planning Project (2020KJRC0040)
DC-bias Optical-Orthogonal Frequency Division Multiplexing (DCO-OFDM) has a high Peak-to-Average Power Ratio (PAPR) and is susceptible to multipath interference and noise frequency bias. To address this challenge, carrier Index Modulation (IM) is introduced into DCO-OFDM and a DCO-OFDM-IM modulation scheme suitable for visible light communication is proposed. In this scheme, the signal mapping constraint model bases on the combination of composite index and Euclidian distance is used to perform block composite index of subcarriers, which can not only transfer information using traditional constellation modulation in the signal domain, but also carry additional information through the carrier index in the frequency domain, which improves effectively the system peak to average ratio and bit error rate performance. The theoretical bit error rate of DCO-OFDM-IM system is derived and verified by monte Carlo method. The results show that compared with traditional DCO-OFDM system, when the number of subcarriers is 256, the modulation order is 4, and the system bit error rate is 10–3, the required Signal-to-Noise Ratio (SNR) of DCO-OFDM-IM system is improved by about 2 dB on average. When the BER is 10–3, the required SNR of the combined index and Euclidian distance algorithm improved by 2 dB on average compared with the random carrier combination system. When the system Complementary Cumulative Distribution Function (CCDF) is 10–1, the average ratio of the original signal peaks of DCO-OFDM-IM is decreased by about 2.4 dB compared with that of DCO-OFDM.
椭圆曲线密码(Elliptic Curve Cryptography, ECC)已经被美国国家标准学会(American National Standards Institute, ANSI)[1]、美国国家标准与技术研究所(National Institute of Standards and Technology, NIST)[2]、电气电子工程师协会(Institute of Electrical and Electronics Engineers, IEEE)[3]等国际标准组织广泛接受和部署[4],应用在各种各样的场景。在比特币的基础技术区块链中,广泛应用ECC中的secp256k1作为区块链的认证机制[5];我国自主研发的密码算法SM2密码标准,是国密体系中重要环节之一。ECC的应用日益增加,不同应用性能需求各异。例如在服务器和大型计算平台等,需要密码芯片具有较高的运算性能。在微控制器等设备中,一般要求密码芯片具有更小的面积。此外不同的标准通常使用不同的椭圆曲线,所以对多种曲线的兼容也一直是椭圆曲线的重点研究目标。
标量乘架构的研究成为热点,Hu等人[6]提出SCA-256曲线的二阶段快速模约简方法,利用半字乘法器5个周期计算大数乘法实现高速标量乘的设计;文献[7]和文献[8]都对wNAF算法进行了优化,降低了标量乘的计算复杂度,提高了标量乘计算速度;Liu等人[9]利用软硬结合的方式以较低的面积实现了支持任意曲线的双域ECC处理器;Hossain等人[10]设计了同时适用于专用集成电路(Application Specific Integrated Circuit, ASIC)和现场可编程逻辑门阵列(Field Programmable Gate Array, FPGA)的标量乘操作步骤,适用于两条曲线;Liu等人[11]优化了非相邻形式算法,以高资源消耗实现了支持P256的高速ECC标量乘设计;Hu等人[12]和Choi等人[13]都提出高度资源复用的设计,以极低的硬件资源实现标量乘法器;Zhang等人[14]改进了蒙哥马利阶梯算法,提出了支持SCA-256的抗功耗攻击的高性能处理器。文献[15]改进了基2交叉模乘算法,提出了一种高面积时间效率的新型标量乘法器架构。这些设计的时间面积(Area·Time, AT)普遍较差,部分仅适用于特定曲线,ECC处理器需要兼顾速度和面积两者之间的关系,为解决此问题本文提出了全新的设计。
标量乘是ECC的核心运算,定义为$kP = P + \cdots + P$。其中$ k $是整数,$ P $是椭圆曲线上一点。标量乘算法较多,主要有二进制标量乘算法、非相邻形式(Non-Adjacent Form, NAF)标量乘算法等[17]。NAF标量乘算法[18]如算法1所示,通过对$ k $进行重新编码,减少$ k $中非0元素出现的次数以达到提高标量乘性能的目的。
YE Xinrong, ZHU Weiping, ZHANG Aiqing, et al. Compressed sensing based on doubly-selective slow-fading channel estimation in OFDM systems[J]. Journal of Electronics &Information Technology, 2015, 37(1): 169–174. doi: 10.11999/JEIT140247
SHAO Kai, JIN Geng, WANG Guangyu, et al. Permutation-mode orthogonal frequency division multiplexing system with index modulation[J]. Journal of Electronics &Information Technology, 2021, 43(9): 2640–2646. doi: 10.11999/JEIT200248
PENG Cong, XU Peng, CHEN Xiang, et al. Influence of independent phase noises on MIMO-OFDM systems[J]. Journal of Electronics &Information Technology, 2017, 39(12): 2999–3003. doi: 10.11999/JEIT170260
[5]
JIANG Tao, TANG Ming, LIN Rui, et al. Investigation of DC-biased optical OFDM with precoding matrix for visible light communications: Theory, simulations, and experiments[J]. IEEE Photonics Journal, 2018, 10(5): 1–16. doi: 10.1109/JPHOT.2018.2866952
[6]
HUSSEIN H S and HAGAG M. Optical MIMO-OFDM with fully generalized index-spatial LED modulation[J]. IEEE Communications Letters, 2019, 23(9): 1556–1559. doi: 10.1109/LCOMM.2019.2926457
ZUO Jiajun, YANG Ruijuan, LI Xiaobai, et al. A compressed sensing method for joint radar and communication system based on OFDM-IM signal[J]. Journal of Electronics &Information Technology, 2020, 42(12): 2976–2983. doi: 10.11999/JEIT190740
GE Lijia, JIANG Zhilin, FENG Sheng, et al. Non-orthogonal-code index modulation[J]. Journal of Electronics &Information Technology, 2018, 40(10): 2331–2336. doi: 10.11999/JEIT180023
[9]
VAN LUONG T and KO Y. Spread OFDM-IM with precoding matrix and low-complexity detection designs[J]. IEEE Transactions on Vehicular Technology, 2018, 67(12): 11619–11626. doi: 10.1109/TVT.2018.2872873
[10]
NTOUN G D, KAPINAS V M, and KARAGIANNIDIS G K. On the optimal tone spacing for interference mitigation in OFDM-IM systems[J]. IEEE Communications Letters, 2017, 21(5): 1019–1022. doi: 10.1109/LCOMM.2017.2660479
[11]
KIM K H. PAPR reduction in OFDM-IM using multilevel dither signals[J]. IEEE Communications Letters, 2019, 23(2): 258–261. doi: 10.1109/LCOMM.2019.2892103
[12]
TUSHA A, DOĞAN S, and ARSLAN H. IQI mitigation for narrowband IoT systems with OFDM-IM[J]. IEEE Access, 2018, 6: 44626–44634. doi: 10.1109/ACCESS.2018.2864892J
[13]
LI Jun, DANG Shuping, WEN Miaowen, et al. Layered orthogonal frequency division multiplexing with index modulation[J]. IEEE Systems Journal, 2019, 13(4): 3793–3802. doi: 10.1109/JSYST.2019.2918068
[14]
QING Hua, YU Hua, LIU Yun, et al. Distributed cooperative OFDM-IM system[J]. China Communications, 2020, 17(9): 167–176. doi: 10.23919/JCC.2020.09.013
ZHAO Hui, MO Jinrong, WANG Wei, et al. Research on nonlinear distortion recovery based on compressed sensing in OFDM system[J]. Journal of Electronics &Information Technology, 2021, 43(7): 1907–1912. doi: 10.11999/JEIT20037
LIU Zhiwei, ZHANG Qi, HUANG Hai, YANG Xiaoqiu, CHEN Guanbai, ZHAO Shilei, YU Bin. Design of High Area Efficiency Elliptic Curve Scalar Multiplier Based on Fast Modulo Reduction of Bit Reorganization[J]. Journal of Electronics & Information Technology, 2024, 46(1): 344-352. doi: 10.11999/JEIT221446
LIU Zhiwei, ZHANG Qi, HUANG Hai, YANG Xiaoqiu, CHEN Guanbai, ZHAO Shilei, YU Bin. Design of High Area Efficiency Elliptic Curve Scalar Multiplier Based on Fast Modulo Reduction of Bit Reorganization[J]. Journal of Electronics & Information Technology, 2024, 46(1): 344-352. doi: 10.11999/JEIT221446