Color image encryption algorithm based on DNA code and alternating quantum random walk

Wang Yi-Nuo; Song Zhao-Yang; Ma Yu-Lin; Hua Nan; Ma Hong-Yang

doi:10.7498/aps.70.20211255

Abstract

In recent years, image encryption technology has attracted much attention. As people pay more attention to communication privacy and network security, the requirements for information encryption technology are more stringent. As one of the information carriers, images are valuable for carrying the effectiveness and vividness of the information. This paper proposes a color image encryption algorithm based on DNA encoding and alternating quantum random walk. Quantum random walk is an excellent cryptographic tool that participates in all parts of the algorithm process, and DNA encoding is used as the core encryption method to complete the algorithm. This article describes the encryption and decryption process in detail, and conducts simulation experiments to verify and analyze the results of the proposed algorithm. In the simulation stage, we design the simulation key parameters, encode the color image encryption and decryption experiments, and carry out related analysis. The experimental results show that the color image encryption algorithm proposed in this paper can perform safe and effective color image encryption. The correlation analysis shows that the image histogram after encryption is stable, the pixel correlation coefficient approaches 0, and the key space is ${2^{ 128 }} $, the three-channel information entropy reaches more than 7.997, which can resist statistical attacks, brute force attacks and other attack methods. In addition, DNA coding has unique biological characteristics in addition to the novel coding and calculation methods, which provide new ideas and directions for cryptographic research.

Keywords:

Authors and contacts

1.
School of Science, Qingdao University of Technology, Qingdao 266520, China
2.
School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China

Corresponding author: Ma Hong-Yang, hongyang_ma@aliyun.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132, 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and the Higher Educational Science and Technology Program of Shandong Province, China(Grant No. J18KZ012).

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References

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Cited By

图 1 双方向格点上交替量子随机行走

Figure 1. Alternating quantum random walking on the bidirectional grid.

DownLoad: Full-Size Img PowerPoint

图 2 算法流程图

Figure 2. Algorithm flowchart

DownLoad: Full-Size Img PowerPoint

图 3 加密算法仿真效果图

Figure 3. Encryption algorithm simulation renderings.

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图 4 Lena图像加密前后相关性分析

Figure 4. Correlation analysis of images before and after Lena encryption.

DownLoad: Full-Size Img PowerPoint

图 6 小猫图像加密前后相关性分析

Figure 6. Correlation analysis of images before and after cat encryption.

DownLoad: Full-Size Img PowerPoint

图 5 蛋糕图像加密前后相关性分析

Figure 5. Correlation analysis of images before and after cake encryption.

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图 7 Lena图像加密前后三通道直方图分析

Figure 7. Analysis of R, G, B three-channel histogram before and after lena image encryption.

DownLoad: Full-Size Img PowerPoint

表 1 8种DNA编码方案

Table 1. Eight DNA coding schemes.

	1	2	3	4	5	6	7	8
A	00	00	01	01	10	10	11	11
G	01	10	00	11	00	11	01	10
C	10	01	11	00	11	00	10	01
T	11	11	10	10	01	01	00	00
注: 满足DNA的生物学特性A-T互补、G-C互补.

DownLoad: CSV

表 2 DNA编码方案1对应的加法方案1

Table 2. Addition plan 1 corresponding to DNA coding plan 1.

+	A	G	C	T
A	A	G	C	T
G	G	C	T	A
C	C	T	A	G
T	T	A	G	C

DownLoad: CSV

表 3 DNA编码方案1对应的减法方案1

Table 3. DNA coding scheme 1 corresponding to subtraction scheme 1.

–	A	G	C	T
A	A	G	C	T
G	T	A	G	C
C	C	T	A	G
T	G	C	T	A

DownLoad: CSV

表 4 像素相关性分析数据

Table 4. Pixel correlation analysis data.

图像	方向	数值
图像	方向	原始图像	加密图像
Lena	水平	0.9275	0.0017
	垂直	0.9603	–0.0005
	对角	0.8941	0.0007
小猫	水平	0.9429	0.0026
	垂直	0.9377	0.0009
	对角	0.9097	–0.0012
蛋糕	水平	0.9229	0.0076
	垂直	0.9056	0.0017
	对角	0.8647	0.0017

DownLoad: CSV

表 5 相关性分析数据对比

Table 5. Correlation analysis data comparison.

算法	通道	平均相关性
本文	Red	水平: 0.0040
	Green	垂直: 0.0010
	Blue	对角: 0.0012
文献[42]	Red	水平: 0.0042
	Green	垂直: 0.0033
	Blue	对角: 0.0024
文献[49]	Red	水平: 0.0025
	Green	垂直: 0.0010
	Blue	对角: 0.0022
文献[50]	Red	水平: 0.0012
	Green	垂直: 0.0011
	Blue	对角: 0.0032

DownLoad: CSV

表 6 密钥敏感性分析数据

Table 6. Key sensitivity analysis data.

图像	通道	NPCR	UACI
Lena	Red	99.6040%	33.4005%
	Green	99.6195%	33.2311%
	Blue	99.5826%	33.5902%
小猫	Red	99.6326%	33.6785%
	Green	99.6124%	33.4455%
	Blue	99.6147%	33.5784%
蛋糕	Red	99.6124%	33.4461%
	Green	99.6528%	33.5315%
	Blue	99.7004%	33.4499%

DownLoad: CSV

表 7 NPCR, UACI数据对比

Table 7. Comparison of NPCR and UACI data.

算法	NPCR平均	UACI平均
本文	99.6257%	33.4835%
文献[42]	99.5506%	33.4055%
文献[49]	99.6554%	33.4675%
文献[50]	99.6150%	33.3900%

DownLoad: CSV

[1]	Zheng R H, Xiao Y, Su S L, Chen Y H, Shi Z C, Song J, Xia Y, Zheng S B 2021 Phys. Rev. A 103 052402 Google Scholar
[2]	Kang Y H, Shi Z C, Huang B H, Song J, Xia Y 2020 Phys. Rev. A 101 032322 Google Scholar
[3]	Long G L 2001 Phys. Rev. A 64 022307 Google Scholar
[4]	Long G L, Li X, Sun Y 2002 Phys. Lett. A 294 143 Google Scholar
[5]	Li T, Zhang S, Fu X Q, Wang X, Wang Y, Lin J, Bao W S 2019 Chin. Phys. B 28 120301 Google Scholar
[6]	Liu F, Zhang X, Xu P A, He Z X, Ma H Y 2020 Int. J. Theor. Phys. 59 3491 Google Scholar
[7]	Zhou N R, Li J F, Yu Z B, Gong L H, A Farouk 2017 Quantum Inf. Process. 16 1 Google Scholar
[8]	Gong L H, Li J F, Zhou N R 2018 Laser Phys. Lett. 15 105204 Google Scholar
[9]	Hu X M, Huang C X, Sheng Y B, Zhou L, Liu B H, Guo Y, Zhang C, Xing W B, Huang Y F, Li C F, Guo G C 2021 Phys. Rev. Lett. 126 010503 Google Scholar
[10]	Zhou L, Sheng Y B, Long G L 2020 Sci. Bull. 65 12 Google Scholar
[11]	Yan Z H, Qin J L, Qin Z Z, Su X L, Jia X J, Xie C D, Peng K C 2021 Fundam. Res. 1 43 Google Scholar
[12]	Zhao J B, Zhang W B, Ma Y L, Zhang X H, Ma H Y 2020 Appl. Sci. 10 1935 Google Scholar
[13]	Qiu T H, Li H, Xie M, Liu Q, Ma H Y 2019 Opt. Express 27 27477 Google Scholar
[14]	Ma H Y, Xu P A, Shao C H, Chen L B, Li J X, Pan Q 2019 Int. J. Theor. Phys. 58 4241 Google Scholar
[15]	Li H S, Fan P, Xia H Y, Peng H L, Long G L 2020 Sci. China Phys. Mech. 63 1
[16]	Zheng R H, Kang Y H, Su S L, Song J, Xia Y 2020 Phys. Rev. A 102 012609 Google Scholar
[17]	Ma H Y, He Z X, Xu P A, Dong Y M, Fan X K 2020 Quantum Inf. Process 19 1
[18]	Xu P A, He Z X, Qiu T H, Ma H Y 2020 Opt. Express 28 12508 Google Scholar
[19]	Zhou N R, Huang L X, Gong L H, Zheng Q W 2020 Quantum Inf. Process. 19 1
[20]	Li H S, Fan P, Xia H Y, Peng H L, Long G L 2020 Sci. China. Phys. Mech. 63 1
[21]	Castagnoli G 2016 Found Phys. 46 360 Google Scholar
[22]	Castagnoli G 2016 Quanta 5 34 Google Scholar
[23]	Gong L H, Song H C, He C S, Liu Y, Zhou N R 2014 Phys. Scr. 89 035101 Google Scholar
[24]	Li H H, Gong L H, Zhou N R 2020 Chin. Phys. B 29 110304 Google Scholar
[25]	Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687 Google Scholar
[26]	Farhi E, Gutmann S 1998 Phys. Rev. A 58 915 Google Scholar
[27]	Watrous J 2001 Comput. Syst. Sci. 62 376 Google Scholar
[28]	Abd El-Latif A A, Abd-El-Atty B, Venegas-Andraca S E, Elwahsh H, Piran M J, Bashir A K, Song O, Mazurczyk W 2020 IEEE Access 8 92687 Google Scholar
[29]	Abd-El-Atty B, Iliyasu A M, Alaskar H, Abd El-Latif A A 2020 Sensors 20 3108 Google Scholar
[30]	Abd EL-Latif A A, Abd-El-Atty B, Venegas-Andraca S E 2020 Physica A 547 123869 Google Scholar
[31]	Abd El-Latif A A, Abd-El-Atty B, Elseuofi S, Khalifa H S, Alghamdi A S, Polat K, Amin M 2020 Physica A 541 123687 Google Scholar
[32]	Abd-El-Atty B, Amin M, Iliyasu A M 2020 Sci. Rep. 10
[33]	Godsil C, Zhan H 2019 J. Comb. Theory Ser. A 167 181 Google Scholar
[34]	Abd-El-Atty B, Iliyasu A M, Alanezi A, Abd EL-Latif A A 2021 Opt. Lasers Eng. 138 106403 Google Scholar
[35]	Adleman L M 1994 Science 266 1021 Google Scholar
[36]	Leier A, Richter C, Banzhaf W, Rauhe H 2000 Biosystems 57 13 Google Scholar
[37]	Chen J 2003 Proceedings of the 2003 International Symposium on Circuits and Systems ISCAS'03. IEEE 2003 3 III-III.
[38]	Chang W L, Guo M, Ho M S H 2005 IEEE Trans Nanobiosci. 4 149 Google Scholar
[39]	Lu M X, Lai X J, Xiao G Z, Qin L 2007 Sci. China Inf. Sci. 50 324 Google Scholar
[40]	Lai X J, Lu M X, Qin L, Han J S, Fang X W 2010 Sci. China Inf. Sci. 53 506 Google Scholar
[41]	Wei X, Guo L, Zhang Q, Zhang J, Lian S G 2012 J. Syst. Softw. 85 290 Google Scholar
[42]	Niu Y, Zhang X, Han F 2017 Comput. Intell. Neurosci. 2017
[43]	Kalsi S, Kaur H, Chang V 2018 J. Med. Syst. 42 1 Google Scholar
[44]	Basu S, Karuppiah M, Nasipuri M, Halder A K, Radhakrishnan 2019 J. Syst. Archit. 94 24 Google Scholar
[45]	Biswas M R, Alam K M R, Tamura S, Morimoto Y 2019 J. Syst. Archit. 48 102363
[46]	Huang L, Wang S, Xiang J, Sun Y 2020 Math. Prob. Eng. 2020
[47]	Alghafis A, Firdousi F, Khan M, Batool A L, Amin M 2020 Math. Comput. Simul. 177 441 Google Scholar
[48]	Eswaran P, Shankar K 2017 Int. J. Pure Appl. Math. 118 393
[49]	Lu Q, Zhu C, Deng X 2020 IEEE Access 8 25664 Google Scholar
[50]	Wang Y, Ye S C, Wang Y 2020 Microelectron. Comput. 37 71

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Vol. 70, Issue 23 - 2021-12-05

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