- ISSN 0258-2724
- CN 51-1277/U
- EI Compendex
- Scopus
- Indexed by Core Journals of China, Chinese S&T Journal Citation Reports
- Chinese S&T Journal Citation Reports
- Chinese Science Citation Database
| Citation: | WANG Yong, WANG Mingyue, GONG Jian. Optimal Design Method of 8 × 8 S-box Based on Multi-objective Genetic Algorithm[J]. Journal of Southwest Jiaotong University, 2024, 59(3): 519-527, 538. doi: 10.3969/j.issn.0258-2724.20210377
|
Chaotic systems have the characteristics of nonlinearity, pseudo-randomness and sensitivity to initial values, which provides an anchor to construct S-boxes based on dynamic system and secures block encryption algorithms. At present, most chaos-based S-box construction methods is designed to optimize single performance index, making it hard to improve the overall performance. To solve this, a new S-box design method is proposed by combining chaotic mapping and multi-objective genetic algorithm. Firstly, the initial S-box population is generated according to the characteristics of chaotic mapping; then, nonlinearity and difference uniformity of S-boxes are optimized under the framework of the genetic algorithm. According to the characteristics of the S-boxes, the exchange operation is introduced into the optimization algorithm, and a new mutation operation and calculation of non-dominated ordered sets are designed, effectively improving the nonlinearity and difference uniformity of the S-boxes. The experimental results show that the difference uniformity of the generated S-box is 6 and its nonlinearity is at least 110, demonstrating an improvement in the overall performance of the S-boxes.
| [1] |
YONG W, PENG L. An improved method to obtaining S-box based on chaos and genetic algorithm[J]. HKIE Transactions, 2012, 19(4): 53-58. doi: 10.1080/1023697X.2012.10669006
|
| [2] |
GUESMI R, BEN FARAH M A, KACHOURI A, et al. A novel design of chaos based S-boxes using genetic algorithm techniques[C]//2014 IEEE/ACS 11th International Conference on Computer Systems and Applications (AICCSA). Doha: IEEE, 2014: 678-684.
|
| [3] |
LIU H J, KADIR A, XU C B. Cryptanalysis and constructing S-box based on chaotic map and backtracking[J]. Applied Mathematics and Computation, 2020, 376: 125153.1-125153.11.
|
| [4] |
韩妍妍,何彦茹,刘培鹤,等. 一种基于混沌系统的ZUC动态S盒构造及应用方案[J]. 计算机研究与发展,2020,57(10): 2147-2157. doi: 10.7544/issn1000-1239.2020.20200466
HAN Yanyan, HE Yanru, LIU Peihe, et al. A dynamic S-box construction and application scheme of ZUC based on chaotic system[J]. Journal of Computer Research and Development, 2020, 57(10): 2147-2157. doi: 10.7544/issn1000-1239.2020.20200466
|
| [5] |
NASEER Y, SHAH T, SHAH D, et al. A novel algorithm of constructing highly nonlinear S-p-boxes[J]. Cryptography, 2019, 3(1): 6. doi: 10.3390/cryptography3010006
|
| [6] |
AZAM N A, HAYAT U, ULLAH I. Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(10): 1378-1389.
|
| [7] |
MILLAN W, CLARK A, DAWSON E. Smart hill climbing finds better Boolean functions[J] .Workshop on Selected Areas in Cryptology Workshop Record, 1997,9: 50-63.
|
| [8] |
JAKIMOSKI G, KOCAREV L. Chaos and cryptography: block encryption ciphers based on chaotic maps[J]. IEEE Transactions on Circuits and Systems Ⅰ: Fundamental Theory and Applications, 2001, 48(2): 163-169. doi: 10.1109/81.904880
|
| [9] |
CASSAL-QUIROGA B B, CAMPOS-CANTÓN E. Generation of dynamical S-boxes for block ciphers via extended logistic map[J]. Mathematical Problems in Engineering, 2020, 2020: 2702653.1-2702653.12.
|
| [10] |
ALZAIDI A A, AHMAD M, DOJA M N, et al. A new 1D chaotic map and β-hill climbing for generating substitution-boxes[J]. IEEE Access, 2018, 6: 55405-55418. doi: 10.1109/ACCESS.2018.2871557
|
| [11] |
ALHADAWI H S, LAMBIĆ D, ZOLKIPLI M F, et al. Globalized firefly algorithm and chaos for designing substitution box[J]. Journal of Information Security and Applications, 2020, 55: 102671.1-102671.13.
|
| [12] |
WANG Y, ZHANG Z Q, ZHANG L Y, et al. A genetic algorithm for constructing bi-jective substitution boxes with high nonlinearity[J]. Information Sciences, 2020, 523: 152-166. doi: 10.1016/j.ins.2020.03.025
|
| [13] |
SILVA-GARCÍA V M, FLORES-CARAPIA R, RENTERÍA-MÁRQUEZ C, et al. Substitution box generation using Chaos: an image encryption application[J]. Applied Mathematics and Computation, 2018, 332: 123-135. doi: 10.1016/j.amc.2018.03.019
|
| [14] |
ALHADAWI H S, MAJID M A, LAMBIĆ D, et al. A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm[J]. Multimedia Tools and Applications, 2021, 80(5): 7333-7350. doi: 10.1007/s11042-020-10048-8
|
| [15] |
ATTAULLA H, JAMAL S S, SHAH T. A novel algebraic technique for the construction of strong substitution box[J]. Wireless Personal Communications, 2018, 99(1): 213-226. doi: 10.1007/s11277-017-5054-x
|
| [16] |
朱虹宏,佟晓筠,张淼,等. 基于动态复合混沌系统的S盒设计[J]. 南京大学学报(自然科学),2018,54(3): 543-547.
ZHU Honghong, TONG Xiaojun, ZHANG Miao, et al. A novel method of designing S-box based on dynamic compound chaotic system[J]. Journal of Nanjing University (Natural Science), 2018, 54(3): 543-547.
|
| [17] |
ULLAH A, JAMAL S S, SHAH T. A novel construction of substitution box using a combination of chaotic maps with improved chaotic range[J]. Nonlinear Dynamics, 2017, 88(4): 2757-2769. doi: 10.1007/s11071-017-3409-1
|
| [18] |
USAMA M, REHMAN O, MEMON I, et al. An efficient construction of key-dependent substitution box based on chaotic sine map[J]. International Journal of Distributed Sensor Networks, 2019, 15(12): 1-9.
|
| [19] |
ÖZKAYNAK F. Construction of robust substitution boxes based on chaotic systems[J]. Neural Computing and Applications, 2019, 31(8): 3317-3326. doi: 10.1007/s00521-017-3287-y
|
| [20] |
TIAN Y, LU Z M. Chaotic S-box: six-dimensional fractional Lorenz—Duffing chaotic system and O-shaped path scrambling[J]. Nonlinear Dynamics, 2018, 94(3): 2115-2126. doi: 10.1007/s11071-018-4478-5
|
| [21] |
陈华,冯登国,吴文玲. 一种改善双射S盒密码特性的有效算法[J]. 计算机研究与发展,2004,41(8): 1410-1414.
CHEN Hua, FENG Dengguo, WU Wenling. An effective algorithm for improving cryptographic properties of bijective S-boxes[J]. Journal of Computer Research and Development, 2004, 41(8): 1410-1414.
|
| [22] |
WANG Y, LEI P, WONG K W. A method for constructing bijective S-box with high nonlinearity based on chaos and optimization[J]. International Journal of Bifurcation and Chaos, 2015, 25(10): 1550127.1-1550127.15
|
| [23] |
PROUFF E. DPA attacks and S-boxes[M]//Fast Software Encryption. Berlin: Springer, 2005: 424-441.
|
| [24] |
ADAMS C, TAVARES S. Good S-boxes are easy to find[J]. Lecture Notes in Computer Science, 1989, 435: 612-615.
|
| [1] | ZHANG Zeqiang, WANG Kaipu, ZHU Lixia, CHENG Wenming. Pareto Hybrid Ant Colony and Genetic Algorithm for Multi-Objective U-Shaped Disassembly Line Balancing Problem[J]. Journal of Southwest Jiaotong University, 2018, 53(3): 628-637, 660. doi: 10.3969/j.issn.0258-2724.2018.03.026 |
| [2] | XIAO Jian, ZHAO Tao. Overview and Prospect of T-S Fuzzy Control[J]. Journal of Southwest Jiaotong University, 2016, 29(3): 462-474. doi: 10.3969/j.issn.0258-2724.2016.03.006 |
| [3] | WANG Hong, DU Weixin, LIU Zhilong, JIANG Zuhua. Bi-level Imperfect Maintenance Strategy and Optimization for Single Component of Electric Multiple Unit[J]. Journal of Southwest Jiaotong University, 2015, 28(4): 683-690. doi: 10.3969/j.issn.0258-2724.2015.04.017 |
| [4] | CHEN Zhiwei, XU Youlin. Fatigue Reliability Analysis of Multi-loading Suspension Bridges Considering Nonlinear Accumulative Damage[J]. Journal of Southwest Jiaotong University, 2014, 27(2): 213-219. doi: 10.3969/j.issn.0258-2724.2014.02.005 |
| [5] | GUO Feng, XIE Jianhua, YUE Yuan. Chaos Control of Lauwerier Mapping[J]. Journal of Southwest Jiaotong University, 2014, 27(3): 525-529. doi: 10.3969/j.issn.0258-2724.2014.03.024 |
| [6] | CUI Bo, ZHANG Jiashu, YANG Yu. Nonlinear Target Tracking Algorithm Based on Block Ensemble Kalman Filter[J]. Journal of Southwest Jiaotong University, 2013, 26(5): 863-869. doi: 10.3969/j.issn.0258-2724.2013.05.013 |
| [7] | PANG Xiaoping, CHEN Jin. Multi-objective Shape Optimization of Hydrodynamic Journal Bearings Using Non-dorminated Sorting Genetic Algorithm Ⅱ[J]. Journal of Southwest Jiaotong University, 2012, 25(4): 639-645. doi: 10.3969/j.issn.0258-2724.2012.04.017 |
| [8] | YOU Wei, FAN Dongming. Nonlinear Least Squares Adjustment Based on Improved Homotopy Algorithm[J]. Journal of Southwest Jiaotong University, 2009, 22(2): 181-185. |
| [9] | LÜ, Xiongwei, LI Jun, LEI Ming, ZHANG Bin. Multi-objective Optimization of Stochastic Demand Inventory Routing Problem with Time Windows[J]. Journal of Southwest Jiaotong University, 2009, 22(2): 289-294. |
| [10] | ZHANG Honghai, HU Minghua. Multi-objection Optimization for Collaborative Scheduling Aircraft Landing on Multi-runways[J]. Journal of Southwest Jiaotong University, 2009, 22(3): 402-409. |
| [11] | ZOU Shurong, HUANG Xiaobin, ZHANG Hongwei. Multi-Objective Genetic Algorithm for Solving Capacitated Vehicle Routing Problems[J]. Journal of Southwest Jiaotong University, 2009, 22(5): 782-786. |
| [12] | SHI Hongguo, PENG Qiyuan, GUO Hanying. Improved Multi-objective GA for MRT Train Operation Simulation Model[J]. Journal of Southwest Jiaotong University, 2006, 19(5): 658-662. |
| [13] | JIADong-li, ZHANG Jia-shu, ZHANG Chao. Geometric Prim itive Extraction Using ChaosGenetic Algorithm[J]. Journal of Southwest Jiaotong University, 2005, 18(4): 496-500. |
| [14] | LIUHai-yan, CHEN Gao-bo, PENG Chuan. Solving Multi-objective Programming Problems with Maximal Entropy Method and Genetic Algorithm[J]. Journal of Southwest Jiaotong University, 2003, 16(1): 8-11. |
| [15] | FENG Chun, CHEN Yong. Genetic Algorithms for Period-Double Bifurcation of Logistic Mapping[J]. Journal of Southwest Jiaotong University, 2003, 16(3): 290-293. |
| [16] | LILi, LIUZhao-hui, CHEN Yong. An Analytic Method for the Synthesis of Spatial 5S-S Parallel Robot Mechanism[J]. Journal of Southwest Jiaotong University, 2002, 15(1): 77-80. |
| [17] | ZHANG Zhi-yuan, HE Chuan. A Genetic Algorithm Based on Uniform Design Paralleled with Genetic Operation[J]. Journal of Southwest Jiaotong University, 2002, 15(5): 536-340. |
| [18] | FENGHao, HEHong-yun, MI Zu-qiang. Nonlinear System Identification with Recurrent Neural Network Based on Genetic Algorithm[J]. Journal of Southwest Jiaotong University, 2002, 15(4): 404-407. |
| [19] | FAN Dong-min. Nonlinear Programming Algorithms for Nonlinear Least Squares Adjustment by Parameters[J]. Journal of Southwest Jiaotong University, 2001, 14(5): 476-481. |
| 1. | 武小年，吴庭，黄昭文，张润莲. 基于混沌映射和NFSR的16比特动态S盒构造方法. 信息安全与通信保密. 2024(11): 10-19 .  |
Figures(10) / Tables(1)
WANG Yong, WANG Mingyue, GONG Jian. Optimal Design Method of 8 × 8 S-box Based on Multi-objective Genetic Algorithm[J]. Journal of Southwest Jiaotong University, 2024, 59(3): 519-527, 538. doi: 10.3969/j.issn.0258-2724.20210377
DownLoad:
