• ISSN 0258-2724
  • CN 51-1277/U
  • EI Compendex
  • Scopus 收录
  • 全国中文核心期刊
  • 中国科技论文统计源期刊
  • 中国科学引文数据库来源期刊

基于二维离散混沌系统和DNA的图像加密方案

徐昌彪 许浩南 明志飞

徐昌彪, 许浩南, 明志飞. 基于二维离散混沌系统和DNA的图像加密方案[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20220810
引用本文: 徐昌彪, 许浩南, 明志飞. 基于二维离散混沌系统和DNA的图像加密方案[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20220810
XU Changbiao, XU Haonan, MING Zhifei. Image Encryption Scheme Based on 2D Discrete Chaotic System and Deoxyribonucleic Acid[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20220810
Citation: XU Changbiao, XU Haonan, MING Zhifei. Image Encryption Scheme Based on 2D Discrete Chaotic System and Deoxyribonucleic Acid[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20220810

基于二维离散混沌系统和DNA的图像加密方案

doi: 10.3969/j.issn.0258-2724.20220810
基金项目: 国家自然科学基金(62071077)
详细信息
    作者简介:

    徐昌彪(1972—),男,教授,博士,研究方向为混沌理论,E-mail:xucb@cqupt.edu.cn

  • 中图分类号: O415.5;TN918.4

Image Encryption Scheme Based on 2D Discrete Chaotic System and Deoxyribonucleic Acid

  • 摘要:

    为丰富低维离散混沌系统的动力学特性以及克服脱氧核糖核酸(deoxyribonucleic acid, DNA)编码的引入使混沌图像加密系统安全性易于降低的问题,基于Arnold映射构建具有恒定正Lyapunov指数的2维离散混沌系统,并将其与DNA编码结合,设计一个混沌图像加密方案. 所设计的混沌系统模型中不含非线性项,系统具有超混沌动力学行为;加密方案中用于加密的混沌序列为明文图像像素与密钥的加取模运算结果,图像按4 × 4大小予以分块,扩散算法中的DNA加减、异或、同或等运算分别基于DNA编码规则1、规则4和规则7. 仿真实验和性能分析结果表明:加密方案的密钥空间达到2266,信息熵为7.9993 bit,密钥灵敏度达到10−15,平均像素变化率(number of pixel change rate, NPCR)、统一平均变化强度(unified average change intensity, UACI)、块平均变化强度(block average change intensity, BACI)分别为99.6092%、33.4664%、26.7718%.

     

  • 图 1  系统相图

    Figure 1.  Phase diagram of the system

    图 2  系统的0-1测试

    Figure 2.  Results of 0-1 test of the system

    图 3  系统Lyapunov指数谱

    Figure 3.  Lyapunov exponential spectrum of the system

    图 4  系统分岔图

    Figure 4.  Bifurcation diagrams of the system

    图 5  系统SE复杂度谱图

    Figure 5.  SE complexity spectrum of the system

    图 6  系统C0复杂度谱图

    Figure 6.  C0 complexity spectrum of the system

    图 7  系统运行时间

    Figure 7.  Running time of the system

    图 8  加密方案流程

    Figure 8.  Flow chart of encryption scheme

    图 9  解密方案流程

    Figure 9.  Flow chart of decryption scheme

    图 10  明文图像与密文图像直方图

    Figure 10.  Histogram of plaintext image and ciphertext image

    图 11  鲁棒性

    Figure 11.  Robustness

    表  1  xnyn的SE、C0测度平均值

    Table  1.   Average of SE and C0 for xn and yn

    参数 xn 的测度平均值yn 的测度平均值
    SEC0SEC0
    a0.94600.25010.94590.2962
    b0.94590.25000.94590.2515
    λ0.94520.25150.94520.2702
    下载: 导出CSV

    表  2  相关系统的模型复杂度与结构复杂度

    Table  2.   Model complexity and structural complexity of related systems

    系统 指标维
    度/维
    参数/个 非线性
    项数/个
    非线性项形式 SE 杂度
    均值
    C0 杂度
    均值
    硬件实现
    难度
    硬件实现
    成本
    本文 2 3 0 0.9457 0.2505
    文献[11] 2 2 1 $x_n^2 $ 0.9460 0.2501
    文献[12] 2 3 1 cos2(carccos xn) 0.9457 0.2499
    文献[13] 4 16 0 0.9460 0.2501
    文献[14] 6 44 0 0.9198 0.1645
    文献[15] 6 36 0 0.9461 0.2501
    下载: 导出CSV

    表  3  DNA编码规则

    Table  3.   DNA encoding rules

    编码规则
    1
    规则
    2
    规则
    3
    规则
    4
    规则
    5
    规则
    6
    规则
    7
    规则
    8
    00AATTGGCC
    01GCGCATAT
    10CGCGTATA
    11TTAACCGG
    下载: 导出CSV

    表  4  本文采用的DNA加法运算规则

    Table  4.   Operation of DNA addition

    项目AGCT
    AAGCT
    GGCTA
    CCTAG
    TTAGC
    下载: 导出CSV

    表  5  本文采用的DNA减法运算规则

    Table  5.   Operation of DNA substraction

    项目AGCT
    AATCG
    GGATC
    CCGAT
    TTCGA
    下载: 导出CSV

    表  6  本文采用的DNA异或运算规则

    Table  6.   Operation of DNA XOR

    项目AGCT
    ACTAG
    GTCGA
    CAGCT
    TGATC
    下载: 导出CSV

    表  7  本文采用的DNA同或运算规则

    Table  7.   Operation of DNA XNOR

    项目AGCT
    AAGCT
    GGATC
    CCTAG
    TTCGA
    下载: 导出CSV

    表  8  加解密方案测试结果

    Table  8.   Test results of encryption and decryption schemes

    下载: 导出CSV

    表  9  信息熵

    Table  9.   Information entropy bit

    方案图像密文明文
    本文Cameraman7.99937.0480
    Lena7.99937.4451
    Mandril7.99937.2925
    文献[16]Lena7.9969
    Cameraman7.9973
    Horse7.9974
    文献[17]Lena7.9977
    Mandril7.9973
    Peppers7.9974
    下载: 导出CSV

    表  10  χ2检验结果

    Table  10.   Test results of χ2 bit

    图像 明文 × 105 密文
    Cameraman 4.1853 248.6660
    Lena 1.5834 256.6152
    Mandril 2.1137 262.8926
    下载: 导出CSV

    表  11  相关性系数计算结果

    Table  11.   Calculation results of correlation coefficient

    方案图像明/密文水平垂直正对角反对角
    本文Cameraman明文0.98810.98400.97950.9779
    密文−0.00270.01010.01240.0069
    Lena明文0.98490.97260.95850.9689
    密文0.01150.03260.0352−0.0252
    Mandril明文0.91220.92200.86920.8592
    密文−0.02950.01350.01750.0294
    文献[16]Lena明文0.92370.94200.8906
    密文0.0040−0.0012−0.0021
    Cameraman明文0.93330.95690.9052
    密文−0.0031−0.00060.0011
    Horse明文0.64250.66820.5179
    密文0.00340.0012−0.0035
    文献[17]Couple明文0.90230.94780.8688
    密文−0.0325−0.00250.0223
    Aerial明文0.88180.89600.7885
    密文0.00690.02210.0172
    Stream and bridge明文0.92580.93870.8958
    密文0.21800.0468−0.0318
    下载: 导出CSV

    表  12  本文所用灰度图像与随机图像间的UACI与BACI值

    Table  12.   UACI and BACI between gray image and random image used in this paper %

    图像 UACI 值 BACI 值
    Cameraman 31.1146 22.8078
    Lena 28.6241 21.3218
    Mandril 27.5411 20.2075
    下载: 导出CSV

    表  13  加解密过程密钥灵敏度分析

    Table  13.   Key sensitivity analysis during encryption and decryption processes %

    参数指标加密过程解密过程
    CameramanLenaMandrilCameramanLenaMandril
    k1 NPCR 99.6090 99.6840 99.6113 99.6090 99.6840 99.6113
    UACI 33.4643 33.4662 33.4725 31.1195 28.6277 27.5460
    BACI 26.7728 26.7719 26.7732 22.8148 21.3235 20.2097
    k2 NPCR 99.6091 99.6099 99.6099 99.6091 99.6099 99.6099
    UACI 33.4637 33.4617 33.4592 31.1154 28.6221 27.5354
    BACI 26.7674 26.7661 26.7693 22.8043 21.3200 20.2060
    k3 NPCR 99.6101 99.6112 99.6103 99.6101 99.6112 99.6103
    UACI 33.4639 33.4655 33.4671 31.1202 28.6278 27.5393
    BACI 26.7738 26.7742 26.7646 22.8075 21.3248 20.2062
    k4 NPCR 99.6086 99.6083 99.6091 99.6086 99.6083 99.6091
    UACI 33.4610 33.4643 33.4641 31.1114 28.6197 27.5388
    BACI 26.7706 26.7708 26.7692 22.8061 21.3174 20.2045
    k5 NPCR 99.6084 99.6112 99.6101 99.6084 99.6112 99.6101
    UACI 33.4664 33.4640 33.4669 31.1209 28.6228 27.5393
    BACI 26.7689 26.7722 26.7703 22.8104 21.3222 20.2043
    r1 NPCR 99.6088 99.6101 99.6111 99.6088 99.6101 99.6111
    UACI 33.4608 33.4679 33.4650 31.1200 28.6299 27.5404
    BACI 26.7701 26.7751 26.7702 22.8104 21.3216 20.2061
    r2 NPCR 99.6101 99.6089 99.6112 99.6101 99.6089 99.6112
    UACI 33.4619 33.4692 33.4615 31.1186 28.6137 27.5363
    BACI 26.7667 26.7729 26.7712 22.8089 21.3215 20.2069
    r3 NPCR 99.6101 99.6089 99.6112
    UACI 31.1189 28.6300 27.5466
    BACI 22.8143 21.3210 20.2117
    r4 NPCR 99.6101 99.6089 99.6112
    UACI 31.1175 28.6251 27.5375
    BACI 22.8048 21.3235 20.2015
    下载: 导出CSV

    表  14  明文敏感性

    Table  14.   Plaintext sensitivity %

    图像 NPCR UACI BACI
    Cameraman 99.6083 33.4632 26.7711
    Lena 99.6106 33.4685 26.7711
    Mandril 99.6087 33.4676 26.7733
    下载: 导出CSV
  • [1] LI W S, YAN W H, ZHANG R X, et al. A new 3D discrete hyperchaotic system and its application in secure transmission[J]. International Journal of Bifurcation and Chaos, 2019, 29(14): 1950206.1-1950206.14.
    [2] RAY A, GHOSH D. Another new chaotic system: bifurcation and chaos control[J]. International Journal of Bifurcation and Chaos, 2020, 30(11): 2050161.1-2050161.13.
    [3] YU F, QIAN S, CHEN X, et al. Chaos-based engineering applications with a 6D memristive multistable hyperchaotic system and a 2D SF-SIMM hyperchaotic map[J]. Complexity, 2021, 2021. 6683284.1- 6683284.21.
    [4] BELAZI A, HERMASSI H, RHOUMA R, et al. Algebraic analysis of a RGB image encryption algorithm based on DNA encoding and chaotic map[J]. Nonlinear Dynamics, 2014, 76(4): 1989-2004. doi: 10.1007/s11071-014-1263-y
    [5] WANG X Y, LI P, ZHANG Y Q, et al. A novel color image encryption scheme using DNA permutation based on the Lorenz system[J]. Multimedia Tools and Applications, 2018, 77(5): 6243-6265. doi: 10.1007/s11042-017-4534-z
    [6] WANG X Y, ZHANG H L, BAO X M. Color image encryption scheme using CML and DNA sequence operations[J]. Biosystems, 2016, 144: 18-26. doi: 10.1016/j.biosystems.2016.03.011
    [7] ZHANG X Q, WANG X S. Multiple-image encryption algorithm based on DNA encoding and chaotic system[J]. Multimedia Tools and Applications, 2019, 78(6): 7841-7869. doi: 10.1007/s11042-018-6496-1
    [8] JITHIN K C, SANKAR S. Colour image encryption algorithm combining Arnold map, DNA sequence operation, and a Mandelbrot set[J]. Journal of Information Security and Applications, 2020, 50: 102428.1-102428.22.
    [9] LIU T M, BANERJEE S, YAN H Z, et al. Dynamical analysis of the improper fractional-order 2D-SCLMM and its DSP implementation[J]. The European Physical Journal Plus, 2021, 136(5): 506.1-506.17.
    [10] AKIF O Z, ALI S, ALI R S, et al. A new pseudorandom bits generator based on a 2D-chaotic system and diffusion property[J]. Bulletin of Electrical Engineering and Informatics, 2021, 10(3): 1580-1588. doi: 10.11591/eei.v10i3.2610
    [11] MERANZA-CASTILLÓN M O, MURILLO-ESCOBAR M A, LÓPEZ-GUTIÉRREZ R M, et al. Pseudorandom number generator based on enhanced Hénon map and its implementation[J]. International Journal of Electronics and Communications, 2019, 107: 239-251. doi: 10.1016/j.aeue.2019.05.028
    [12] LIU Y, QIN Z, LIAO X F, et al. A chaotic image encryption scheme based on Hénon-Chebyshev modulation map and genetic operations[J]. International Journal of Bifurcation and Chaos, 2020, 30(6): 2050090.1-2050090.22. doi: 10.1142/S021812742050090X
    [13] KANSO A, GHEBLEH M, ALAZEMI A. Efficient image encryption scheme based on 4-dimensional chaotic maps[J]. Informatica, 2020, 31(4): 793-820.
    [14] WANG Y J, WU C C, KANG S Q, et al. Multi-channel chaotic encryption algorithm for color image based on DNA coding[J]. Multimedia Tools and Applications, 2020, 79(25): 18317-18342.
    [15] SUN C Y, WANG E F, ZHAO B. Image encryption scheme with compressed sensing based on a new six-dimensional non-degenerate discrete hyperchaotic system and plaintext-related scrambling[J]. Entropy, 2021, 23(3): 291.1-291.25.
    [16] ZHANG S J, LIU L F. A novel image encryption algorithm based on SPWLCM and DNA coding[J]. Mathematics and Computers in Simulation, 2021, 190: 723-744. doi: 10.1016/j.matcom.2021.06.012
    [17] TIAN J F, LU Y, ZUO X Y, et al. A novel image encryption algorithm using PWLCM map-based CML chaotic system and dynamic DNA encryption[J]. Multimedia Tools and Applications, 2021, 80(21): 32841-32861.
    [18] KANG X J, GUO Z H. A new color image encryption scheme based on DNA encoding and spatiotemporal chaotic system[J]. Signal Processing: Image Communication, 2020, 80: 115670-115681. doi: 10.1016/j.image.2019.115670
    [19] WANG C F, FAN C L, FENG K, et al. Analysis of the time series generated by a new high-dimensional discrete chaotic system[J]. Complexity, 2018, 2018: 1-11.
    [20] SUN K H, LIU X, ZHU C X. The 0-1 test algorithm for chaos and its applications[J]. Chinese Physics B, 2010, 19(11): 204-210.
    [21] 叶晓林,牟俊,王智森,等. 基于SE和C0算法的连续混沌系统复杂度分析[J]. 大连工业大学学报,2018,37(1): 67-72.

    YE Xiaolin, MOU Jun, WANG Zhisen, et al. Analysis of continuous chaotic complexity based on SE and C0 algorithm[J]. Journal of Dalian Polytechnic University, 2018, 37(1): 67-72.
    [22] 孙克辉. 混沌保密通信原理与技术[M]. 北京: 清华大学出版社, 2015: 30-33.
  • 加载中
图(11) / 表(14)
计量
  • 文章访问数:  93
  • HTML全文浏览量:  84
  • PDF下载量:  24
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-11-21
  • 修回日期:  2023-02-20
  • 网络出版日期:  2023-12-19

目录

    /

    返回文章
    返回