基于时变互耦合双混沌系统的轻量级序列密码

doi:10.3969/j.issn.1671-1122.2024.03.005

摘要/Abstract

摘要：

文章针对资源受限的物联网环境下的数据加密传输问题，设计了一种基于时变互耦合双混沌系统的轻量级序列密码。以Tent和Arnold混沌映射为基础，通过引入累加器和耦合项，构造一种用于序列密码内部状态更新的时变双混沌系统，基于位操作，对密钥流输出部分进行设计。文章对算法的基本运算、参数、精度、实现方式和策略进行设计并在FPGA上实现，硬件资源消耗为2370个等效门，密钥流输出速率为1.68 bit/clk。分析表明，该密码具有良好的安全性和抗攻击能力，与ISO/IEC标准的轻量级序列密码相比，安全性、资源消耗和吞吐量均有显著优势。

关键词: 物联网, 双混沌系统, 轻量级, 退化, 序列密码

Abstract:

Aiming at the problem of data encryption transmission in the resource-limited Internet of Things environment, this paper designed a lightweight stream cipher based on time-varying mutual coupling double chaotic system. Based on the chaotic maps of Tent and Arnold, a time-varying double chaotic system for updating the internal state of stream cipher is constructed by introducing accumulators and coupling terms. Based on bit operation, the output part of key stream is designed. This paper designed the basic operation, parameters, accuracy, implementation mode and strategy of the algorithm and implemented it on FPGA. The consumption of hardware resources is 2370 GE, and the output rate of key stream is 1.68bit/clk. The analysis shows that this cipher has good security and anti-attack ability. Compared with the lightweight stream ciphers of ISO/IEC standard, it has obvious advantages in security, resource consumption and throughput.

Key words: Internet of things, double chaotic system, lightweight, degenerate, stream cipher

中图分类号:

TP309

杨杰超, 胡汉平, 帅燕, 邓宇昕. 基于时变互耦合双混沌系统的轻量级序列密码[J]. 信息网络安全, 2024, 24(3): 385-397.

YANG Jiechao, HU Hanping, SHUAI Yan, DENG Yuxin. Lightweight Stream Cipher Based on Time-Varying Mutual Coupling Double Chaotic System[J]. Netinfo Security, 2024, 24(3): 385-397.

图/表 26

图1

图2

图3

图4

图5

图6

图7

表1

表2

图8

图9

图10

图11

图12

图13

表3

表4

图14

图15

表5

表6

图16

图17

表7

表8

表9

参考文献 37

[1]	SHANNON C E. Communication Theory of Secrecy Systems[J]. Bell Systems Technical Journal, 1949, 28(4): 656-715. doi: 10.1002/bltj.1949.28.issue-4 URL
[2]	JOHN A, REDDY S K M, JOSE J. Fault Resistan Trivium-Like Stream Cipher Using Higher Radii Cellular Automata[J]. Journal of Cellular Automata, 2022, 16(5-6): 463-490.
[3]	MA Zhen, TIAN Tian, QI Wenfeng. A New Distinguishing Attack on Grain-V1 with 111 Initialization Rounds[J]. Journal of Systems Science & Complexity, 2019, 32(3): 970-984.
[4]	ALAMER A, SOH B, BRUMBAUGH D E. MICKEY 2.0.85: A Secure and Lighter MICKEY 2.0 Cipher Variant with Improved Power Consumption for Smaller Devices in the IoT[J]. SYMMETRY-BASEL, 2020, 12(1): 1-21.
[5]	ISO/IEC 29192-3: 2012(E) Information Technology-Security Techniques Lightweight Cryptography-Part 3: Stream Ciphers[S]. Switzerland: ISO, 2012.
[6]	GUAN Jie, DING Lin, ZHANG Kai. Analysis and Design of Stream Cryptography[M]. Beijing: Science Press, 2019.
	关杰, 丁林, 张凯. 序列密码分析与设计[M]. 北京: 科学出版社, 2019.
[7]	ANANTHARAMAN R, SULE V. Observer Attack on Stream Ciphers[J]. Ifac Papersonline, 2022, 55(30): 13-18.
[8]	SINHA N. Internal State Recovery of Espresso Stream Cipher Using Conditional Sampling Resistance and Tmdto Attack[J]. Advances in Mathematics of Communications, 2021, 15(3): 539-556. doi: 10.3934/amc.2020081 URL
[9]	MING Hao, HU Hanping, XIE Xuhui, et al. DCC-128: A Hardware-Oriented Lightweight Chaotic Stream Cipher[J]. Nonlinear Dyn, 2023, 111: 21995-22011. doi: 10.1007/s11071-023-09035-z
[10]	HAMANN M, KRAUSE M, MEIER W, et al. Design and Analysis of Small-State Grain-Like Stream Ciphers[J]. Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences, 2018, 10(5): 803-834.
[11]	WANG Shichang, LIU Meicheng, LIN Dongdai, et al. On Grain-Like Small State Stream Ciphers against Fast Correlation Attacks: Cryptanalysis of Plantlet, Fruit-v2 and Fruit-80[J]. Computer Journal, 2023, 66(6): 1376-1399.
[12]	LI Tianyan, YORKE J A. Period Three Implies Chaos[J]. Amer Math Monthly, 1975, 82(10): 985-992. doi: 10.1080/00029890.1975.11994008 URL
[13]	DEVANEY R L. An Introduction to Chaotic Dynamical Systems[M]. New Jersey: Addison-Wesley, 1989.
[14]	ROBERT A, MATTHEWS J. On the Derivation of a “Chaotic” Encryption Algorithm[J]. Cryptologia, 1989, 13(1): 29-42. doi: 10.1080/0161-118991863745 URL
[15]	KOCAREV L. Chaos-Based Cryptograph: A Brief Overview[J]. IEEE Circuits and Systems Magazine, 2001, 1(3): 6-21.
[16]	BARRETO E, HUNT B R, GREBOGI C, et al. From High Dimensional Chaos to Stable Periodic Orbits: The Structure of Parameter Space[J]. Physical Review Letters, 1997, 78: 4561-4564. doi: 10.1103/PhysRevLett.78.4561 URL
[17]	PAREEK N K, VINOD P, SUD K K. Image Encryption Using Chaotic Logistic Map[J]. Image and Vision Computing, 2006, 24(9): 926-934. doi: 10.1016/j.imavis.2006.02.021 URL
[18]	ZHONG Jin, JIANG Dong, HUANG Qiguo, et al. A Self-Updating Digital Chaotic Stream Cipher[J]. International Journal of Modern Physics C, 2018, 29(8): 1-22.
[19]	LAHCENE M, NOUREDDINE C, LORENZ P, et al. Securing Information Using a Proposed Reliable Chaos-Based Stream Cipher: with Real-Time FPGA-Based Wireless Connection Implementation[J]. Nonlinear Dyn, 2002, 11(1): 801-830.
[20]	ZHANG Hangming, HU Hanping, DING Weiping. Image Encryption Algorithm Based on Hilbert Sorting Vector and New Spatiotemporal Chaotic System[J]. Optics & Laser Technology, 2023, 167: 1-20.
[21]	ZHAO Mingchao, WANG Kaihua, FU Xinchu. The Dynamical Properties of 2-D Coupled Logistic Map and Applications to Stream Cipher[J]. Communication on Applied Mathematics and Computation, 2009, 23(1): 87-92.
[22]	LI Ruisong, ZHAO Yu. Note on Chaos of a Coupled Lattice System Related with the Belusov-Zhabotinskii Reaction[J]. Journal of Mathematical Chemistry, 2020, 58(6): 1306-1311. doi: 10.1007/s10910-020-01122-5
[23]	JOTHI V B S, SELVARAJ S, CHINNATHAMBI V, et al. Bifurcations and Chaos in Two-Coupled Periodically Driven Four-Well Duffing-Van der Pol Oscillators[J]. Chinese Journal of Physics, 2017, 55(5): 1849-1856. doi: 10.1016/j.cjph.2017.08.008 URL
[24]	AKHAVAN A, MOBARAKI A, LIM S C, et al. Pseudo Random Number Generator Based on Quantum Chaotic Map[J]. Communications in Nonlinear Science and Numerical Simulation, 2014, 19(1): 101-111. doi: 10.1016/j.cnsns.2013.06.017 URL
[25]	GEOFFREY R G. Chaotic Dynamics-Fractals Tilings and Substitutions[M]. Cambridge: Cambridge University Press, 2017.
[26]	HEIDEL J. The Existence of Periodic Orbits of the Tent Map[J]. Physics Letters A, 1990, 143: 195-201. doi: 10.1016/0375-9601(90)90738-A URL
[27]	ARNOLD A, AVEZ A. Ergodic Problems of Classical Mechanics[M]. New Jersey: Addison-Wesley, 1967.
[28]	GONG Lihua, QIU Kaide, DENG Chengzhi, et al. An Image Compression and Encryption Algorithm Based on Chaotic System and Compressive Sensing[J]. Optics and Laser Technology, 2019, 115: 257-267. doi: 10.1016/j.optlastec.2019.01.039 URL
[29]	WANG Xingyuan, FENG Le, ZHAO Hongyu. Fast Image Encryption Algorithm Based on Parallel Computing System[J]. Journal of Information Science, 2019, 486: 340-358.
[30]	HU Hanping, YU Rongjie, MING Hao, et al. A Coupled Chaotic System and Its Application: China, CN113190865A[P]. 2021-07-30.
[31]	ZHENG Jun, HU Hanping. A Novel Method of Constructing High-Dimensional Digital Chaotic Systems on Finite-State Automata[J]. Chinese Physics B, 2020, 29(9): 1-11.
[32]	FENG Dengguo. Analysis Method of Stream Cipher[M]. Beijing: Tsinghua Press, 2021.
	冯登国. 序列密码分析方法[M]. 北京: 清华大学出版社, 2021.
[33]	YAHYA W A, OYEWUMI K J, SEN K D. Information and Complexity Measures for the Ring-Shaped Modified Kratzer Potential[J]. India Journal of Chemistry Section A-Inorganic Bio-Inorganic Physical Theoretical & Analytical Chemisty, 2014, 53(10): 1307-1316.
[34]	HU Yusong, JUNG C L, QIN Qipu, et al. HDVC: Deep Video Compression with Hyperprior-Based Entropy Coding[J]. IEEE Assess, 2024, 12: 17541-17551.
[35]	ANDREW R, JUAN S, JAMES N. et al. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications[R]. USA: National Institute of Standards and Technology, Special Publication 800-22, 2010.
[36]	ECUYER P L, SIMARD R J. Testu01: A C Library for Empirical Testing of Random Number Generators[J]. ACM Transactions on Mathematical Software, 2007, 33(4): 1-40.
[37]	DHANDA S S, SINGH B, JINDAL P. Lightweight Cryptography: A Solution to Secure IoT[J]. Wireless Personal Communications, 2020, 112: 1947-1980. doi: 10.1007/s11277-020-07134-3

使用资源	用量
端口数量	355个
线网数量	1561个
单元数量	1042个
组合单元数量	833个
连续单元数量	202个
缓冲器和反相器数量	102个
基准电路数量	1个
组合面积	10866.969730 μm²
非组合面积	7053.150047 μm²
总芯片面积	17920.119777 μm²

混沌系统		Tent映射	第一维	第二维	第三维	第四维
控制参数		μ=1-2^-6	a=1,b=1	c=1,d=2	μ₁=1-2^-5	μ₂=1-2^-6
李亚普诺夫指数	时变耦合	0.684	0.626	0.628	0.643	0.643
李亚普诺夫指数	固定耦合	0.684	0.561	0.577	0.567	0.556
内部状态长度	时变耦合	2¹⁶比特	2¹³¹比特
内部状态长度	固定耦合	2¹⁶比特	2⁶⁴比特
初始空间长度	时变耦合	2¹⁶比特	2¹²⁸比特
初始空间长度	固定耦合	2¹⁶比特	2⁶⁴比特
轨道周期长度	时变耦合	9280比特	大于1.6?10¹³比特
轨道周期长度	固定耦合	9280比特	115660172368比特

种子密钥	初始化变量	改变方式	改变后种子密钥	密钥流改变量	密钥流改变率
13FB	x₁	1→0	13FA	49999460	49.999460%
DE6A	x₂	0→1	DE6B	50003451	50.003451%
0CBD	x₃	1→0	0CBC	50005016	50.005016%
9722	x₄	0→1	9723	49999600	49.999600%
52A6	q₁	0→1	52A7	49998474	49.998474%
8518	q₂	0→1	8519	49999658	49.999658%
1121	q₃	1→0	1120	49999813	49.999813%
89A0	q₄	0→1	89A1	49996088	49.996088%

测试项	p值	通过率	测试结果
频率测试	0.572847	991/1000	通过
块内频率测试	0.725829	982/1000	通过
累计和测试	0.810790	990/1000	通过
游程测试	0.705466	990/1000	通过
块内最长游程测试	0.514124	992/1000	通过
二进制矩阵测试	0.357000	992/1000	通过
离散傅里叶变换测试	0.729870	987/1000	通过
非重叠模版匹配测试	0.491260	990/1000	通过
重叠模版匹配测试	0.078567	987/1000	通过
Maurer通用统计测试	0.792508	987/1000	通过
近似熵测试	0.473064	990/1000	通过
随机偏离测试	0.426830	616/621	通过
随机偏离变量测试	0.613539	615/621	通过
串行测试	0.251078	983/1000	通过
线性复杂度测试	0.761719	984/1000	通过

数据长度/比特	Alphabit	Rabbit	BlockAlphabit
2²⁰	17/17	38/38	102/102
2²⁵	17/17	39/39	102/102
2³²	17/17	40/40	102/102