计算机科学 ›› 2018, Vol. 45 ›› Issue (11A): 393-397.

• 信息安全 • 上一篇    下一篇

基于分数阶Fourier的双混沌加密算法

汪乐乐, 李国东   

  1. 新疆财经大学应用数学学院 乌鲁木齐830012
  • 出版日期:2019-02-26 发布日期:2019-02-26
  • 通讯作者: 李国东(1976-),男,博士,教授,主要研究方向为数字分析与图像处理,E-mail:lgdzhy@126.com
  • 作者简介:汪乐乐(1993-),女,硕士,主要研究方向为数字分析与图像处理,E-mail:1491658722@qq.com
  • 基金资助:
    本文受国家自然科学基金(11461063),国家社科基金(14BTJ021),新疆维吾尔自治区普通高等学校人文社会科学重点研究基地基金(050315B03),新疆财经大学研究生科研创新项目(XJUFE2017K006,XJGRI2017112),新疆维吾尔自治区自然科学基金(2017D01A24,2017D01A23)资助。

Double Chaotic Image Encryption Algorithm Based on Fractional Transform

WANG Le-le, LI Guo-dong   

  1. School of Mathematics,Xinjiang University of Finance and Economics,Urumqi 830012,China
  • Online:2019-02-26 Published:2019-02-26

摘要: 图像加密在生活中有着重要地位。针对传统的自然混沌系统安全性较低的问题,提出了改进的H-L双混沌和分数阶Fourier变换的图像加密算法。以穷举法解出的最优解序列的顺序为基础,将混沌映射与分数阶Fourier变换结合起来,实现了空间域和频域的置乱,使明文信息得到了隐藏。仿真实验结果表明,通过改进的算法达到了较好的加密效果,其密钥空间大、计算复杂度低、敏感性强,能有效地抵抗统计攻击等,在图形信息安全方面有一定的应用价值。

关键词: 背包问题, 分数阶Fourier, 混沌加密, 离散余弦变换, 图像加密

Abstract: Image encryption plays an important role in daily life.Aiming at the problem of low security of traditional natural chaos system,an improved image encryption algorithm based on H-L double chaos and fractional Fourier transformwas proposed.Based on the order of the optimal solution sequence solved by the exhaustive method,the chaotic map is combined with the fractional Fourier transform.At the same time,it combines with the fractional Fourier transform to realize the scrambling in the spatial and the frequency domains,so that the plain text information is hidden.The simulation results show that the improved algorithm achieves good encryption effect,large key space,low computational complexity,strong sensitivity and effective anti-statistical attack performance.It has certain value in the aspect of gra-phic information security.

Key words: Backpack problem, Chaotic encryption, DCT, Fractional Fourier, Image encryption

中图分类号: 

  • TP309
[1]ADLEMAN L M.Molecular Computation of Solutions to Combinatorial Problems [J].Science,1994,266(5187):1021-1024.
[2]黄冬梅,耿霞,魏立斐.基于Henon映射的加密遥感图像的安全检索方案 [J].软件学报,2016,27(7):1729-1740.
[3]赵国敏,李国东.基于广义 Henon映射以及CNN超混沌系统图像加密方案 [J].信阳师范学院学报自然科学版,2015,15(1):141-145.
[4]黄清梅,李国东.基于CNN超混沌特性对图像加密技术的应用研究 [J].绵阳师范学院学报,2017,2(2):60-66.
[5]谢国波,杨彬.基于比特置乱的量子混沌图像加密算法[J].计算机工程,2017,43(7):182-186.
[6]谢国波,王添.基于像素置乱和比特替换的混沌图像加密算法[J].微电子学与计算机,2016,33(3):80-85.
[7]徐兵,袁立.基于改进Logistic混沌映射的数字图像加密算法研究[J].计算机测量与控制,2014,22(7):165-167.
[8]郭伟创,叶瑞松.一种基于猫映射和伯努利移位映射的图像加密算法[J].汕头大学学报(自然科学版),2015,30(1):13-23.
[9]张雪锋,范九伦.一种改进的基于混沌系统的数字图像加密算法[J].计算机应用研究,2007,24(4):184-186.
[10]郑凡,田小建,范文华,等.基于Henon映射的数字图像加密[J].北京邮电大学学报,2008,31(1):66-70.
[11]韩凤英,李云.利用复合混沌系统的图像加密方案研究与设计[J].电脑知识与技术,2010,6(13):3450-3452.
[12]李凯佳,俞锐刚,袁凌云.基于DNA-记忆元胞自动机与Hash函数的图像加密算法 [J].计算机工程与设计,2017,38(2):470-477.
[13]廖春成,周小平,廖春龙,等.像素位置与比特双重置乱的混沌图像加密算法 [J].中国科技论文,2014(1):112-116.
[14] WANG X Y,WANG T.A novel algorithm for image encryption based on couple chaotic systems [J].International Journal of Modern Physics B,2012,26(30):395.
[15]GANESAN K,MURALI K.Image encryption using eight di-mensional chaotic cat map [J].European Physical Journal Special Topics,2014,223(8):1611-1622.
[16]CHENG P,YANG H,WEI P,et al.A fast image encryption algorithm based on chaotic map and lookup table [J].Nonlinear Dynamics,2014,79(3):2121-2131.
[17]LI G D,WANG L L.Double chaotic image encryption algorithm based on optimal sequence solution and fractional transform[J].Visual Computer,2018,1(1):1-11.
[1] 周连兵, 周湘贞, 崔学荣.
基于双重二维混沌映射的压缩图像加密方案
Compressed Image Encryption Scheme Based on Dual Two Dimensional Chaotic Map
计算机科学, 2022, 49(8): 344-349. https://doi.org/10.11896/jsjkx.210700235
[2] 张赛男, 李千目.
一种基于Logistic-Sine-Cosine映射的彩色图像加密算法
Color Image Encryption Algorithm Based on Logistic-Sine-Cosine Mapping
计算机科学, 2022, 49(1): 353-358. https://doi.org/10.11896/jsjkx.201000041
[3] 班多晗, 吕鑫, 王鑫元.
基于一维混沌映射的高效图像加密算法
Efficient Image Encryption Algorithm Based on 1D Chaotic Map
计算机科学, 2020, 47(4): 278-284. https://doi.org/10.11896/jsjkx.190600059
[4] 禹峰,龚馨慧,王世红.
基于快速置换和可选择像素扩散的医疗图像加密算法的安全性分析
Cryptanalysis of Medical Image Encryption Algorithm Using High-speed Scrambling and Pixel Adaptive Diffusion
计算机科学, 2020, 47(2): 276-280. https://doi.org/10.11896/jsjkx.190100051
[5] 田军锋, 彭静静, 左宪禹, 葛强, 范明虎.
基于循环移位和多混沌映射的图像加密算法
Image Encryption Algorithm Based on Cyclic Shift and Multiple Chaotic Maps
计算机科学, 2020, 47(10): 327-331. https://doi.org/10.11896/jsjkx.190800003
[6] 王丽娟, 李国东, 吕冬梅.
基于动态参数控制的混沌系统图像加密算法
Chaotic System Image Encryption Algorithm Based on Dynamic Parameter Control
计算机科学, 2019, 46(11A): 469-472.
[7] 韩雪娟, 李国东, 王思秀.
基于Logistic和超混沌结合的加密算法
Cryptographic Algorithm Based on Combination of Logistic and Hyperchaos
计算机科学, 2019, 46(11A): 477-482.
[8] 赵方正, 李成海, 刘晨, 宋亚飞.
超混沌彩色图像加密算法优化及安全性分析
Security Analysis and Optimization of Hyper-chaotic Color Image Encryption Algorithm
计算机科学, 2019, 46(11A): 483-487.
[9] 高思齐,邢玉轩,肖侬,刘芳.
求解01背包问题的贪婪蛙跳算法
Greedy Frog Leaping Algorithm for 01 Knapsack Problem
计算机科学, 2018, 45(7): 73-77. https://doi.org/10.11896/j.issn.1002-137X.2018.07.011
[10] 于阳,于洪涛,黄瑞阳.
基于多重信任的协同过滤推荐算法
Collaborative Filtering Recommendation Algorithm Based on Multiple Trust
计算机科学, 2018, 45(5): 108-115. https://doi.org/10.11896/j.issn.1002-137X.2018.05.019
[11] 朱淑芹,王文宏,李俊青.
针对基于感知器模型的混沌图像加密算法的选择明文攻击
Chosen Plaintext Attack on Chaotic Image Encryption Algorithm Based on Perceptron Model
计算机科学, 2018, 45(4): 178-181. https://doi.org/10.11896/j.issn.1002-137X.2018.04.030
[12] 汪乐乐, 李国东.
基于游程性序列的双重混沌的图像加密算法
Double Chaotic Image Encryption Algorithm Based on Run-length Sequence
计算机科学, 2018, 45(11A): 361-366.
[13] 臧睿, 于洋.
基于对合矩阵的复合图像加密算法
Composite Image Encryption Algorithm Based on Involutory Matrix
计算机科学, 2018, 45(11A): 389-392.
[14] 朱淑芹,李俊青.
参数扰动下的混沌的图像加密方案
Image Encryption Scheme Based on Chaos with Parameter Perturbation
计算机科学, 2017, 44(Z6): 356-360. https://doi.org/10.11896/j.issn.1002-137X.2017.6A.081
[15] 朱淑芹,王文宏,孙忠贵.
对一种基于比特置乱的超混沌图像加密算法的选择明文攻击
Chosen Plaintext Attack on Image Encryption Algorithm Based on Bit Scrambling and Hyperchaos
计算机科学, 2017, 44(11): 273-278. https://doi.org/10.11896/j.issn.1002-137X.2017.11.041
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!