基于變步長約瑟夫遍歷和DNA動態(tài)編碼的圖像加密算法

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doi:10.11999/JEIT190849

基于變步長約瑟夫遍歷和DNA動態(tài)編碼的圖像加密算法

doi: 10.11999/JEIT190849 cstr: 32379.14.JEIT190849

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張勛才^2, ,

1.
鄭州輕工業(yè)大學建筑環(huán)境工程學院鄭州 450002
2.
鄭州輕工業(yè)大學電氣信息工程學院鄭州 450002

基金項目: 國家自然科學基金(61602424, U1804262)，河南省重點研發(fā)與推廣專項(202102210177, 192102210134)

詳細信息

作者簡介:
?，摚号?，1982年生，副教授，研究方向為生物信息處理與信息安全

張勛才：男，1981年生，副教授、研究方向為智能信息處理與優(yōu)化控制

通訊作者:
張勛才　zhangxuncai@pku.edu.cn

中圖分類號: TP301; TN918.4
計量
- 文章訪問數(shù): 3584
- HTML全文瀏覽量: 1140
- PDF下載量: 171
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2019-10-31
- 修回日期: 2020-05-03
- 網(wǎng)絡(luò)出版日期: 2020-05-19
- 刊出日期: 2020-06-22

Image Encryption Algorithm of Based on Variable Step Length Josephus Traversing and DNA Dynamic Coding

Ying NIU¹,
Xuncai ZHANG^{2
, ,}

1.
College of Architecture Environment Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China
2.
College of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China

Funds: The National Natural Science Foundation of China (61602424, U1804262), The Key Research and Development Program of Henan Province (202102210177, 192102210134)

摘要

摘要: 數(shù)字圖像傳輸和存儲的安全問題已成為信息安全研究的熱點。該文提出一種基于變步長約瑟夫遍歷和DNA動態(tài)編碼的圖像加密方法。首先將混沌映射產(chǎn)生的隨機序列作為約瑟夫遍歷的變步長，改進約瑟夫遍歷問題，并采用改進的約瑟夫遍歷對圖像像素位置進行置亂；其次，動態(tài)選擇DNA編碼規(guī)則，對圖像像素進行DNA編碼，并與給定的DNA序列進行堿基運算；DNA編碼規(guī)則的動態(tài)選擇，很好地解決了DNA編碼規(guī)則少所帶來的安全隱患，提高了算法的安全性。最后通過密文反饋和混沌系統(tǒng)迭代來進一步增強算法的混淆和擴散特性。實驗和安全性分析結(jié)果表明，該算法不僅對密鑰的敏感性強，而且能有效抵御統(tǒng)計性分析和窮舉分析等攻擊操作。
- 圖像加密 /
- DNA動態(tài)編碼 /
- 約瑟夫遍歷 /
- 置換
Abstract: The security of digital image transmission and storage has become a hotspot of information security research. An image encryption algorithm based on variable step length Josephus traversing and DNA dynamic coding is proposed. Firstly, through the thorough analysis of Joseph traversing, the random sequence generated by chaotic map is taken as the variable step length of Joseph traversing, and the pixel position is permutated. Secondly, according to the random sequence generated by chaotic map, the DNA coding rules of pixel points transformation are selected, and the image is dynamically encoded into DNA strand, and the DNA sequence is calculated based on the principle of complementary base pairing. Because the DNA coding rules of the pixels transformation are dynamic, the hidden danger caused by the lack of DNA coding rules is well solved, and the security of the algorithm is improved. Finally, the permutation and diffusion characteristics of the algorithm are further enhanced by ciphertext feedback and chaotic system iteration. Experiment and security analysis results show that the algorithm not only has large key space and strong sensitivity to keys, but also can effectively resist attacks such as statistical analysis and brutal analysis.
- Image encryption /
- Dynamic DNA encoding /
- Josephus traversing /
- Displace

HTML全文

圖 1 約瑟夫置亂效果

下載: 全尺寸圖片幻燈片

圖 2 加密流程圖

下載: 全尺寸圖片幻燈片

圖 3 原始圖像和密文圖像

下載: 全尺寸圖片幻燈片

圖 4 原始圖像和密文圖像的直方圖統(tǒng)計

下載: 全尺寸圖片幻燈片

圖 5 被裁剪的密文圖像和解密圖像

下載: 全尺寸圖片幻燈片

表 1 8種編碼規(guī)則

	1	2	3	4	5	6	7	8
00	A	A	C	G	C	G	T	T
01	C	G	A	A	T	T	C	G
10	G	C	T	T	A	A	G	C
11	T	T	G	C	G	C	A	A

下載: 導出CSV

表 2 異或運算規(guī)則

XOR	A	C	G	T
A	A	C	G	T
C	C	A	T	G
G	G	T	A	C
T	T	G	C	A

下載: 導出CSV

表 3 加法運算規(guī)則

ADD	A	C	G	T
A	A	C	G	T
C	C	G	T	A
G	G	T	A	C
T	T	A	C	G

下載: 導出CSV

表 4 減法運算規(guī)則

SUB	A	C	G	T
A	A	T	G	C
C	C	A	T	G
G	G	C	A	T
T	T	G	C	A

下載: 導出CSV

表 5 加密密鑰敏感性(%)

初始值	NPCR	UACI
$ {x}'_{0} $+10^–10	99.5956	33.5652
$ {y}'_{0} $+10^–10	99.6109	33.3368
$ {z}'_{0} $+10^–10	99.6261	33.5378

下載: 導出CSV

表 6 密鑰的解密敏感性分析(%)

初始值	NPCR	UACI
$ {x}'_{0} $+10^–10	99.6048	34.6094
$ {y}'_{0} $+10^–10	99.5956	34.4388
$ {x}'_{0} $+10^–10	99.5529	34.5867

下載: 導出CSV

表 7 原始圖像發(fā)生微小改變時NPCR和UACI的值(%)

圖像	NPCR	UACI
Lena	99.5378	33.3080
Cameraman	99.6209	33.5080
Brain	99.5375	33.6244
White	99.6284	33.8780

下載: 導出CSV

表 8 直方圖的χ²分布統(tǒng)計

	原始圖像χ²分布	密文圖像χ²分布	檢測結(jié)果
Lena	39851.3281	239.0847	通過
Cameraman	161271.875	212.0456	通過
Brain	1044635.67	258.3025	通過

下載: 導出CSV

表 9 原始圖像和密文圖像各方向的相關(guān)系數(shù)

圖像	相關(guān)系數(shù)
	原始圖像			密文圖像
	水平方向	垂直方向	對角線方向	水平方向	垂直方向	對角線方向
Cameraman	0.9540	0.9087	0.8813	–0.0070	0.0083	0.0013
Brain	0.9965	0.9959	0.9942	–0.0038	0.0051	0.0042

下載: 導出CSV

表 10 原始圖像和密文圖像的信息熵

圖像	信息熵
圖像	原始圖像	密文圖像
Lena	6.8794	7.9873
Cameraman	6.9046	7.9976
Brain	5.0329	7.9970
White	0	7.9970

下載: 導出CSV

表 11 Cameraman圖像遭受數(shù)據(jù)丟失攻擊后解密圖像的各項指標

裁剪面積	相關(guān)性			NPCR	UACI
裁剪面積	水平	垂直	對角線	NPCR	UACI
原圖	0.9501	0.9231	0.9011	0	0
1/64	0.9145	0.8689	0.8649	1.7548	0.6277
1/16	0.8075	0.7754	0.7442	6.6223	2.3429
1/4	0.4667	0.4507	0.4352	25.7019	9.0683

下載: 導出CSV

表 12 常用加密算法的安全性能列舉

Cameraman	NPCR (%)	UACI(%)	信息熵	相關(guān)系數(shù)
Cameraman	NPCR (%)	UACI(%)	信息熵	水平	垂直	對角線
文獻[18]	99.5986	33.4561	7.9971	0.0047	–0.0066	0.0031
文獻[21]	99.5620	31.1169	–	–	–	–
文獻[19]	99.6047	33.5050	7.9963	–0.0074	0.0069	–0.0191
本文方法	99.6277	33.5715	7.9971	–0.0070	0.0083	0.0013

下載: 導出CSV

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