基于gyrator变换和矢量分解的非对称图像加密方法

姚丽莉; 袁操今; 强俊杰; 冯少彤; 聂守平

doi:10.7498/aps.65.214203

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摘要

本文结合矢量分解和gyrator变换的数学实现得到了一种新的非对称图像加密算法，它将待加密图像先通过矢量分解加密到两块纯相位板中，然后利用从gyrator变换的数学实现中推导出来的加密算法加密其中一块相位板，获得最终的实值密文.另一块相位板作为解密密钥.算法的解密密钥不同于加密密钥，实现了非对称加密，加密过程中产生的两个私钥增大了算法的安全性.数值模拟结果验证了该算法的可行性和有效性.

关键词:

作者及机构信息

1.
南京师范大学, 江苏省光电技术重点实验室, 南京 210023

通信作者: 袁操今, optyuan@163.com

基金项目: 国家自然科学基金（批准号：61377003）、南京师范大学高层次人才科研启动项目（批准号：184080H20162）、南京师范大学青年领军人才培养项目（批准号：184080H20178）和江苏省高校自然科学研究重大项目（批准号：14KJA140001）资助的课题.

参考文献

[1]	Refregier P, Javidi B 1995 Opt. Lett. 20 767
[2]	Deng X P, Zhao D M 2012 Opt. Lasers Technol. 44 136
[3]	Abuturab M R 2015 Opt. Lasers Eng. 69 49
[4]	Liu Z J, Guo C, Tan J B, Liu W, Wu J J, Wu Q, Pan L Q, Liu S T 2015 Opt. Lasers Eng. 68 87
[5]	Sui L S, Xin M T, Tian A L, Jin H Y 2013 Opt. Lasers Eng. 51 1297
[6]	Chen W, Chen X 2012 Appl. Opt. 51 6076
[7]	Rajput S K, Nishchal N K 2013 Appl. Opt. 52 4343
[8]	Peng X, Zhang P, Wei H Z, Yu B 2006 Acta Phys. Sin. 55 1130(in Chinese)[彭翔, 张鹏, 位恒政, 于斌2006物理学报55 1130]
[9]	Peng X, Wei H Z, Zhang P 2007 Acta Phys. Sin. 56 3924(in Chinese)[彭翔, 位恒政, 张鹏2007物理学报56 3924]
[10]	Frauel Y, Castro A, Naughton T J, Javidid B 2007 Opt. Express 15 10253
[11]	Qin W, Peng X 2010 Opt. Lett. 35 118
[12]	Rajput S K, Nishchal N K 2012 Appl. Opt. 51 5377
[13]	Rajput S K, Nishchal N K 2014 J. Opt. Soc. Am. A 31 1233
[14]	Mehra I, Nishchal N K 2015 Opt. Commun. 354 344
[15]	Abuturab M R 2014 Opt. Lasers Eng. 58 39
[16]	Abuturab M R 2014 Opt. Commun. 323 100
[17]	Abuturab M R 2015 Opt. Lasers Eng. 69 49
[18]	Rajput S K, Nishchal N K 2014 Appl. Opt. 53 418
[19]	Wang Y, Quan C, Tay C J 2016 Opt. Lasers Eng. 78 8
[20]	Wang X G, Zhao D M 2011 Opt. Commun. 284 945
[21]	Joshi M, Shakher C, Singh K 2009 Opt. Lasers Eng. 47 721
[22]	Zhou N R, Wang Y X, Gong L H 2011 Opt. Commun. 284 3234
[23]	Rodrigo J A, Alieva T, Calvo M L 2007 Opt. Express 15 2190
[24]	Liu Z, Chen D, Ma J, Wei S, Zhang Y, Dai J 2011 Optik 122 864
[25]	Zhang Y, Xiao D 2013 Opt. Lasers Eng. 51 472

施引文献

[1]	Refregier P, Javidi B 1995 Opt. Lett. 20 767
[2]	Deng X P, Zhao D M 2012 Opt. Lasers Technol. 44 136
[3]	Abuturab M R 2015 Opt. Lasers Eng. 69 49
[4]	Liu Z J, Guo C, Tan J B, Liu W, Wu J J, Wu Q, Pan L Q, Liu S T 2015 Opt. Lasers Eng. 68 87
[5]	Sui L S, Xin M T, Tian A L, Jin H Y 2013 Opt. Lasers Eng. 51 1297
[6]	Chen W, Chen X 2012 Appl. Opt. 51 6076
[7]	Rajput S K, Nishchal N K 2013 Appl. Opt. 52 4343
[8]	Peng X, Zhang P, Wei H Z, Yu B 2006 Acta Phys. Sin. 55 1130(in Chinese)[彭翔, 张鹏, 位恒政, 于斌2006物理学报55 1130]
[9]	Peng X, Wei H Z, Zhang P 2007 Acta Phys. Sin. 56 3924(in Chinese)[彭翔, 位恒政, 张鹏2007物理学报56 3924]
[10]	Frauel Y, Castro A, Naughton T J, Javidid B 2007 Opt. Express 15 10253
[11]	Qin W, Peng X 2010 Opt. Lett. 35 118
[12]	Rajput S K, Nishchal N K 2012 Appl. Opt. 51 5377
[13]	Rajput S K, Nishchal N K 2014 J. Opt. Soc. Am. A 31 1233
[14]	Mehra I, Nishchal N K 2015 Opt. Commun. 354 344
[15]	Abuturab M R 2014 Opt. Lasers Eng. 58 39
[16]	Abuturab M R 2014 Opt. Commun. 323 100
[17]	Abuturab M R 2015 Opt. Lasers Eng. 69 49
[18]	Rajput S K, Nishchal N K 2014 Appl. Opt. 53 418
[19]	Wang Y, Quan C, Tay C J 2016 Opt. Lasers Eng. 78 8
[20]	Wang X G, Zhao D M 2011 Opt. Commun. 284 945
[21]	Joshi M, Shakher C, Singh K 2009 Opt. Lasers Eng. 47 721
[22]	Zhou N R, Wang Y X, Gong L H 2011 Opt. Commun. 284 3234
[23]	Rodrigo J A, Alieva T, Calvo M L 2007 Opt. Express 15 2190
[24]	Liu Z, Chen D, Ma J, Wei S, Zhang Y, Dai J 2011 Optik 122 864
[25]	Zhang Y, Xiao D 2013 Opt. Lasers Eng. 51 472

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基于gyrator变换和矢量分解的非对称图像加密方法

1. 南京师范大学, 江苏省光电技术重点实验室, 南京 210023

通信作者: 袁操今, optyuan@163.com

基金项目:

国家自然科学基金（批准号：61377003）、南京师范大学高层次人才科研启动项目（批准号：184080H20162）、南京师范大学青年领军人才培养项目（批准号：184080H20178）和江苏省高校自然科学研究重大项目（批准号：14KJA140001）资助的课题.

收稿日期: 2016-06-15

修回日期: 2016-07-06

刊出日期: 2016-11-05

摘要: 本文结合矢量分解和gyrator变换的数学实现得到了一种新的非对称图像加密算法，它将待加密图像先通过矢量分解加密到两块纯相位板中，然后利用从gyrator变换的数学实现中推导出来的加密算法加密其中一块相位板，获得最终的实值密文.另一块相位板作为解密密钥.算法的解密密钥不同于加密密钥，实现了非对称加密，加密过程中产生的两个私钥增大了算法的安全性.数值模拟结果验证了该算法的可行性和有效性.

关键词:

Asymmetric image encryption method based on gyrator transform and vector operation

1.
Key Laboratory for Opto-Electronic Technology of Jiangsu Province, Nanjing Normal University, Nanjing 210023, China

Fund Project:

Project supported by the National Natural Science Foundation of China(Grant No. 61377003), the Scientific Research Foundation for Advanced Talents, Nanjing Normal University, China(Grant No. 184080H20162), the Training Program Foundation for Youth Leader Talents by Nanjing Normal University, China(Grant No. 184080H20178), and the Major Natural Science Research Project for Universities of Jiangsu Province, China(Grant No. 14KJA140001).

Received Date: 15 June 2016

Accepted Date: 06 July 2016

Published Online: 05 November 2016

Abstract: With the rapid development of computer network technology, information security has attracted increasing attention. Due to the characteristics of multi-dimensional operation and parallel processing capability, optical image encryption techniques have been receiving more and more attention. Since the well-known double random phase encoding technique was proposed, many other methods based on optical information processing means such as the use of optical transform, interference, and polarized light encoding, have been proposed for optical image encryption. However, recent researches have demonstrated that traditional optical encryption techniques are symmetric cryptosystems, in which decryption keys are identical to encryption keys and they have been found to be vulnerable to different types of attacks, such as known plaintext and chosen plaintext attacks. To overcome this shortcoming, asymmetric cryptosystems based on nonlinear phase-truncation techniques and phase retrieval algorithm have been proposed. Asymmetric cryptosystem is a cryptographic system in which encryption keys are different from decryption keys. The encryption keys are used as public keys which are disseminated widely, and the decryption keys are used as private keys which are known only to the authorized users. So, asymmetric cryptosystem can offer a higher-level security than symmetric cryptosystem. However, asymmetric cryptosystems based on phase retrieval algorithms require a lot of computational time, and asymmetric cryptosystems based on phase-truncated Fourier transforms have been found to be vulnerable to special attack. Therefore, in this paper, a novel asymmetric image encryption method is proposed by using the gyrator transform and vector operation. The original image is encrypted into two phase masks with vector operation. One is a random phase mask and the other is a phase mask related to the original image. In the encryption process, the random phase mask is used as a phase key and the other phase mask is transformed by gyrator transform. The transform result is performed by Fourier transform after being modulated by a phase distribution. The ciphertext is the amplitude of the above result. Compared with previous encryption schemes, the suggested method has two advantages. Firstly, we have proposed a new asymmetric encryption method based on the gyrator transform and vector operation. The decryption process is different from the encryption process. The gyrator transform and Fourier transform are used in the encryption process, while only the inverse operation of Fourier transform is employed in the decryption process. In addition, the decryption keys produced in the encryption process are different from the encryption keys. Therefore, the proposed scheme has high resistance against the conventional attacks. Secondly, the encrypted result is real-valued, which is convenient for display, transmission and storage.Numerical simulations illustrate the feasibility and effectiveness of the proposed encryption scheme.

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