CN103955883A - Asymmetric double-image encryption method based on fractional Fourier domain phase recovery procedure - Google Patents
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Abstract
基于分数傅里叶域相位恢复过程的非对称双图像加密方法,包括纯相位提取,相位调制,分数傅里叶变换步骤。本发明将基于分数傅里叶域相位恢复过程的非对称加密方法应用于双图像加密,加密过程与解密过程不同,且加密密钥不同于解密密钥,解决了传统对称加密算法易于攻击、加密密钥与解密密钥相同的缺点;通过攻击测试,证明本发明不仅对于暴力攻击的抵抗力强、而且对于噪声与其他的特定攻击的抵抗力也很强。同时,本发明的密钥空间大,解决了传统加密算法密钥空间不足的问题。本发明解密过程可通过光学方法实现,系统简单,操作方便。
An asymmetric dual-image encryption method based on a phase recovery process in the fractional Fourier domain, including pure phase extraction, phase modulation, and fractional Fourier transform steps. The present invention applies the asymmetric encryption method based on the fractional Fourier domain phase recovery process to double image encryption, the encryption process is different from the decryption process, and the encryption key is different from the decryption key, which solves the problem that the traditional symmetric encryption algorithm is easy to attack and encrypt The key has the same disadvantage as the decryption key; through the attack test, it is proved that the present invention not only has strong resistance to brute force attack, but also has strong resistance to noise and other specific attacks. At the same time, the key space of the present invention is large, which solves the problem of insufficient key space of traditional encryption algorithms. The decryption process of the invention can be realized by optical method, the system is simple and the operation is convenient.
Description
技术领域technical field
本发明属于虚拟光学信息加密方法技术领域,涉及一种基于分数傅里叶域相位恢复过程的非对称双图像加密方法。The invention belongs to the technical field of virtual optical information encryption methods, and relates to an asymmetric double-image encryption method based on a fractional Fourier domain phase recovery process.
背景技术Background technique
随着互联网的迅速普及,图像作为当代社会非常有效率的信息携带者已经被广泛的用于各种各样的领域,图像加密问题成为信息安全领域中一个重要的领域。自Refregier和Javidi提出经典的基于双随机相位加密(DRPE)技术以来,在过去十几年间,许多基于傅里叶变换域、分数傅里叶变换域、菲涅尔域、GT域的加密及认证系统已经被纷纷提出。而且Alfalou和Brosseau指出:这些技术同时可以用作压缩操作。虽然大多数已经发布的基于DRPE的光学加密系统对于信号处理拥有优秀的对于平行的、多维的处理能力。但是我们应该指出,所有这些策略都属于对称密码系统的范畴,加密密钥同时用作解密密钥。一些研究调查表明:这些策略由于它们数学及光学转换上固有的线性属性,很容易受到攻击。为抵抗这些攻击,Qin和Peng提出一种基于相位截断傅里叶变换(PTFT)的非对称密码系统,这种策略的加密密钥不同于解密密钥,通过使用非线性的相位截断操作来避免密码系统的线性属性。With the rapid popularization of the Internet, images, as a very efficient information carrier in contemporary society, have been widely used in various fields, and image encryption has become an important field in the field of information security. Since Refregier and Javidi proposed the classic double random phase encryption (DRPE) technology, in the past ten years, many encryption and authentication based on Fourier transform domain, fractional Fourier transform domain, Fresnel domain, GT domain systems have been proposed. Moreover, Alfalou and Brosseau point out: these techniques can also be used as compression operations. Although most of the published DRPE-based optical encryption systems have excellent parallel and multi-dimensional processing capabilities for signal processing. But we should point out that all these strategies fall under the category of symmetric cryptosystems, where the encryption key is simultaneously used as the decryption key. Several research investigations have shown that these strategies are vulnerable due to their inherently linear properties in mathematics and optical transformations. To resist these attacks, Qin and Peng proposed an asymmetric cryptosystem based on phase truncated Fourier transform (PTFT). The encryption key of this strategy is different from the decryption key, which is avoided by using a nonlinear Linearity properties of cryptosystems.
最近,自从司徒国海和赵道木提出多图像加密技术,基于多路技术的多图像加密技术在信息安全领域得到越来越多的关注。Alfalou和Mansour提出两个安全层的加密方案,第一层用相位恢复过程来复用和同时加密目标图像,第二层用到双随机相位系统来加密图像。在之后的工作里,Alfalou等人利用离散余弦变换同时进行压缩与加密多幅图像的工作。王小刚和赵道木提出基于叠加原理和全息图的全相位图像加密方案,该方案将实值的原始图像加密成纯相位函数(POF)。邓晓鹏和赵道木提出使用傅里叶域相位恢复过程和相位调制的多图像加密方法,该方法完全避免串扰噪声的影响。Hwang Hone-Ene等人提出在菲涅尔域基于改进的Gerchberg–Saxton算法(MGSA)的彩色图像加密方案,显著地降低串扰噪声对图像信息的干扰。Recently, since Situ Guohai and Zhao Daomu proposed multi-image encryption technology, multi-image encryption technology based on multiplex technology has received more and more attention in the field of information security. Alfalou and Mansour proposed an encryption scheme with two security layers. The first layer uses the phase recovery process to multiplex and simultaneously encrypt the target image, and the second layer uses a double random phase system to encrypt the image. In subsequent work, Alfalou et al. used discrete cosine transform to simultaneously compress and encrypt multiple images. Wang Xiaogang and Zhao Daomu proposed an all-phase image encryption scheme based on the superposition principle and hologram, which encrypted the real-valued original image into a pure phase function (POF). Deng Xiaopeng and Zhao Daomu proposed a multi-image encryption method using Fourier domain phase recovery process and phase modulation, which completely avoids the influence of crosstalk noise. Hwang Hone-Ene et al proposed a color image encryption scheme based on the improved Gerchberg–Saxton algorithm (MGSA) in the Fresnel domain, which can significantly reduce the interference of crosstalk noise on image information.
双图像加密作为多图像加密的一个特例,在光学加密系统中也吸引了很大的关注。李慧娟和王玉荣提出基于迭代Gyrator变换的双图像加密,用不同组Gyrator变换角度同时将两幅原始加密成一幅密文图像。李慧娟等人做的工作是,将两幅图像分别加密到一个复函数的实部与虚部。王小刚和赵道木提出基于相位恢复算法与PTFT的将两幅欲加密的图像加密进一幅明面上的图像,在该方法中加密密钥不同于解密密钥。然而,王小刚和赵道木设计一种特殊的攻击,这种攻击使用两步迭代振幅恢复法。在这种攻击之下,当加密密钥作为公钥时,加密信息会被显露出来。随后,王小刚和赵道木提出另一种对这种攻击有很强抵抗性的一种双图像加密技术。之后,李慧娟和王玉荣提出基于离散分数随机变换和混沌映射的双图像加密技术,该技术可以提高在加密、存储、转换时的效率。肖迪等人提出基于离散Chirikov标准映射的双图像光学加密,该方法中,两幅原始图像分别作为复函数的振幅和相位,使用Chirikov标准映射置乱该复函数后,在基于混沌的离散分数随机变换和二维混沌随机掩码的作用下得到最终密文。上述算法虽然在一定程度上简化了加密过程,但依然存在安全性低、密钥空间小、收敛速度慢等问题。As a special case of multi-image encryption, dual-image encryption has also attracted great attention in optical encryption systems. Li Huijuan and Wang Yurong proposed double-image encryption based on iterative Gyrator transformation, using different sets of Gyrator transformation angles to simultaneously encrypt two original images into one ciphertext image. The work done by Li Huijuan and others is to encrypt two images to the real part and imaginary part of a complex function respectively. Wang Xiaogang and Zhao Daomu proposed to encrypt two images to be encrypted into one bright image based on phase recovery algorithm and PTFT. In this method, the encryption key is different from the decryption key. However, Wang Xiaogang and Zhao Daomu devise a special attack that uses a two-step iterative amplitude recovery method. Under this attack, when the encryption key is used as the public key, the encrypted information will be revealed. Subsequently, Wang Xiaogang and Zhao Daomu proposed another double-image encryption technology that is highly resistant to this attack. Later, Li Huijuan and Wang Yurong proposed a dual-image encryption technology based on discrete fractional random transformation and chaotic mapping, which can improve the efficiency of encryption, storage, and conversion. Xiao Di and others proposed dual-image optical encryption based on discrete Chirikov standard mapping. In this method, the two original images are used as the amplitude and phase of the complex function respectively. After using the Chirikov standard mapping to scramble the complex function, the discrete fraction based on chaos The final ciphertext is obtained under the effect of random transformation and two-dimensional chaotic random mask. Although the above algorithm simplifies the encryption process to a certain extent, there are still problems such as low security, small key space, and slow convergence speed.
发明内容Contents of the invention
本发明的目的是提出一种基于分数傅里叶域相位恢复过程的非对称双图像加密方法,解决现有技术存在的安全性低、易受到攻击的问题。The purpose of the present invention is to propose an asymmetric double-image encryption method based on the phase recovery process in the fractional Fourier domain to solve the problems of low security and vulnerability to attack in the prior art.
本发明所采用的技术方案是,基于分数傅里叶域相位恢复过程的非对称双图像加密方法,包括纯相位提取,相位调制,分数傅里叶变换步骤。具体包括如下步骤:The technical scheme adopted in the present invention is an asymmetric double-image encryption method based on the fractional Fourier domain phase recovery process, including pure phase extraction, phase modulation, and fractional Fourier transform steps. Specifically include the following steps:
第一步,纯相位提取:有两幅原始灰度图像,使用分数傅里叶域相位恢复过程提取第i(i=1,2)幅灰度图像fi(i=1,2)的纯相位函数exp(jξi,1)(i=1,2);在使用分数傅里叶域相位恢复过程提取原始灰度图像fi(i=1,2)的纯相位函数过程中,伴随产生相位模板函数φi,1,φi,2,ξi,2(i=1,2);The first step, pure phase extraction: there are two original grayscale images, use the fractional Fourier domain phase recovery process to extract the pure phase of the i (i=1,2) grayscale image fi ( i =1,2) Phase function exp(jξ i,1 )(i=1,2); in the process of extracting the pure phase function of the original grayscale image f i (i=1,2) using the fractional Fourier domain phase recovery process, the concomitant generation Phase template function φ i,1 ,φ i,2 ,ξ i,2 (i=1,2);
第二步,相位调制:在临时图像生成模块中,一个复矩阵Hi(i=1,2)通过振幅图像g与相应的两个相位函数ξi,1,ξi,2产生The second step, phase modulation: in the temporary image generation module, a complex matrix H i (i=1,2) is generated through the amplitude image g and the corresponding two phase functions ξ i,1 , ξ i,2
Hi=Fβ2{Fβ1[gexp(jξi,1)]exp(jξi,2)} (1)H i =F β2 {F β1 [gexp(jξ i,1 )]exp(jξ i,2 )} (1)
进行相位调制,两个Hi通过卷积运算被组合进一个矩阵HFor phase modulation, two H i are combined into a matrix H by convolution operation
H=H1*H2 (2)式(1)、(2)中j为虚部符号,exp{·}为指数运算,g为相位图像,Fα表示分数傅里叶变换,ξi,1、ξi,2是相位函数,H为调制结果,*表示卷积运算;H=H 1 *H 2 (2) j in formula (1) and (2) is the symbol of imaginary part, exp{ } is exponent operation, g is phase image, F α represents fractional Fourier transform, ξ i, 1. ξi ,2 is the phase function, H is the modulation result, and * means the convolution operation;
第三步,分数傅里叶变换:对第二步得到的调制结果H实施α3阶分数傅里叶变换得到计算矩阵的振幅即为密文Cfinal,解密密钥φi,d也被同时生成:The third step, fractional Fourier transform: implement α 3rd order fractional Fourier transform on the modulation result H obtained in the second step to obtain calculate Amplitude of matrix That is, the ciphertext C final , and the decryption key φ i,d is also generated at the same time:
其中,|H|表示组合矩阵的振幅,j为虚部符号,exp{·}为指数运算,arg{·}表示矩阵的相位。Among them, |H| represents the amplitude of the combined matrix, j is the symbol of the imaginary part, exp{·} is the exponent operation, and arg{·} represents the phase of the matrix.
分数傅里叶域相位恢复过程使用三个相位模版函数,φi,1,φi,2,ξi,1,(i=1,2)即为该过程的三个相位模版函数;The fractional Fourier domain phase recovery process uses three phase template functions, φ i,1 ,φ i,2 ,ξ i,1 , (i=1,2) are the three phase template functions of the process;
上述加密方法的解密过程具体为,将最终密文Cfinal和乘上相位函数exp(jφi,d)生成复矩阵对实施-(α2+α3)阶逆分数傅里叶变换得到调制后的结果Hi,由Hi和相位矩阵exp(jφi,2)相乘得到hi,对hi实施-α1阶逆分数傅里叶变换得到然后提取的振幅作为解密图像fi,即:The decryption process of the above encryption method is specifically to multiply the final ciphertext C final by the phase function exp(jφ i,d ) to generate a complex matrix right Implement the -(α 2 +α 3 ) order inverse fractional Fourier transform to obtain the modulated result H i , multiply H i and the phase matrix exp(jφ i,2 ) to obtain h i , implement -α 1 on h i Order inverse fractional Fourier transform to get then extract The amplitude of the decrypted image f i , namely:
fi=|F-α1{F-(α2+α3)[Cfinalexp(jφi,d)]}expj(φi,2)| (4)f i =|F -α1 {F -(α2+α3) [C final exp(jφ i,d )]}expj(φ i,2 )| (4)
上述解密方法所用的解密装置包括两个空间光调制器和两个透镜,两个空间光调制器和两个透镜间隔排列;两个空间光调制器为空间光调制器PM1和空间光调制器PM2,两个透镜为透镜L1和透镜L2;透镜L1设置在空间光调制器PM1和空间光调制器PM2之间,透镜L2设置在空间光调制器PM2于解密图像之间,空间光调制器PM1和空间光调制器PM2与电子控制器连接,电子控制器通过计算机与解密图像连接。The decryption device used in the above decryption method includes two spatial light modulators and two lenses, and the two spatial light modulators and the two lenses are arranged at intervals; the two spatial light modulators are spatial light modulator PM1 and spatial light modulator PM2 , the two lenses are lens L1 and lens L2; lens L1 is arranged between spatial light modulator PM1 and spatial light modulator PM2, lens L2 is arranged between spatial light modulator PM2 and the decrypted image, spatial light modulator PM1 and The spatial light modulator PM2 is connected with the electronic controller, and the electronic controller is connected with the decrypted image through a computer.
将空间光调制器PM1和空间光调制器PM2分别设置为exp(jφi,d)和exp(jφi,2),解密过程以密文图像Cfinal作为入射光输入,使用空间光调制器PM1调制密文图像Cfinal,调制的图像透过透镜L1实现-(α2+α3)阶分数傅里叶变换;使用空间光调制器PM2调制-(α2+α3)阶分数傅里叶变换的结果,调制后的图像透过透镜L2实现-α1阶分数傅里叶变换,即可获得原始的明文图像fi。Set the spatial light modulator PM1 and the spatial light modulator PM2 as exp(jφ i,d ) and exp(jφ i,2 ) respectively, the decryption process takes the ciphertext image C final as the incident light input, and uses the spatial light modulator PM1 Modulate the ciphertext image C final , and the modulated image passes through the lens L1 to realize -(α 2 +α 3 ) order fractional Fourier transform; use the spatial light modulator PM2 to modulate -(α 2 +α 3 ) order fractional Fourier transform As a result of the transformation, the modulated image undergoes -α 1st -order fractional Fourier transformation through the lens L2, and the original plaintext image f i can be obtained.
上述解密方法也可以使用光电混合装置来实现,光电混合装置包括两个掩膜和两个透镜,两个掩膜和两个透镜间隔排列;两个掩膜为掩膜exp(jφi,d)和掩膜exp(jφi,2),两个透镜为透镜L1和透镜L2;透镜L1设置在掩膜exp(jφi,d)和掩膜exp(jφi,2)之间,透镜L2设置在掩膜掩膜exp(jφi,2)与解密图像之间,掩膜exp(jφi,d)和掩膜exp(jφi,2)与电子控制器连接,电子控制器通过计算机与CCD图像传感器连接,由CCD上可以获取解密图像。The above-mentioned deciphering method can also be realized using a photoelectric hybrid device, which includes two masks and two lenses, and the two masks and the two lenses are arranged at intervals; the two masks are mask exp(jφ i,d ) and mask exp(jφ i,2 ), the two lenses are lens L1 and lens L2; lens L1 is set between mask exp(jφ i,d ) and mask exp(jφ i,2 ), lens L2 is set Between the mask exp(jφ i,2 ) and the decrypted image, the mask exp(jφ i,d ) and the mask exp(jφ i,2 ) are connected to the electronic controller, and the electronic controller communicates with the CCD through the computer The image sensor is connected, and the decrypted image can be obtained from the CCD.
本发明具有如下有益效果:The present invention has following beneficial effects:
1、本发明的加密过程与解密过程不同,加密密钥不同于解密密钥,避免了非对称加密算法加密密钥与解密密钥相同、易受攻击的缺点,提高了安全性。1. The encryption process of the present invention is different from the decryption process, and the encryption key is different from the decryption key, which avoids the disadvantage that the encryption key of the asymmetric encryption algorithm is the same as the decryption key and is vulnerable to attacks, and improves security.
2、通过攻击测试,证明本发明不仅对于暴力攻击的抵抗力强,而且对于噪声与其他的特定攻击的抵抗力也很强。非法用户无法通过攻击图像获取任何有价值的信息。2. Through the attack test, it is proved that the present invention not only has strong resistance to brute force attack, but also has strong resistance to noise and other specific attacks. Illegal users cannot obtain any valuable information by attacking images.
3、本发明加密方法解决了现有加密系统密钥空间小的问题,提高了密钥空间。通过统计分析,对于密钥φi,d,密钥空间约为S1≈116256×256;φi,2的密钥空间约为S1≈6256×256。由于加密系统的密钥空间为S1×S2,因此,本发明具有足以对抗暴力攻击的足够大的密钥空间。3. The encryption method of the present invention solves the problem of small key space in the existing encryption system and improves the key space. Through statistical analysis, for the key φ i,d , the key space is approximately S 1 ≈116 256×256 ; the key space of φ i,2 is approximately S 1 ≈6 256×256 . Since the key space of the encryption system is S 1 ×S 2 , the present invention has a sufficiently large key space against brute force attacks.
4、本发明加密方法同时提高了收敛速度。现有的单通道加密方法的收敛次数为400次左右,而本发明加密方法的收敛次数大约为40次,收敛速度有明显提高。4. The encryption method of the present invention improves the convergence speed at the same time. The convergence times of the existing single-channel encryption method are about 400 times, while the convergence times of the encryption method of the present invention are about 40 times, and the convergence speed is obviously improved.
5、本发明解密过程可通过光学方法实现,系统简单,操作方便。5. The decryption process of the present invention can be realized by optical method, the system is simple and the operation is convenient.
附图说明Description of drawings
图1是本发明基于分数傅里叶域相位恢复过程的非对称双图像加密方法原理图。FIG. 1 is a schematic diagram of an asymmetric double-image encryption method based on a phase recovery process in the fractional Fourier domain of the present invention.
图2是本发明基于分数傅里叶域相位恢复过程的非对称双图像加密方法加密过程图。Fig. 2 is a diagram of the encryption process of the asymmetric double-image encryption method based on the fractional Fourier domain phase recovery process of the present invention.
图3是本发明基于分数傅里叶域相位恢复过程的非对称双图像加密方法解密过程图。Fig. 3 is a diagram of the decryption process of the asymmetric double-image encryption method based on the phase recovery process in the fractional Fourier domain of the present invention.
图4是本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法装置结构示意图。Fig. 4 is a schematic structural diagram of an asymmetric double-image decryption method device based on a phase recovery process in the fractional Fourier domain of the present invention.
图5是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的原始图像“Zelda”。Fig. 5 is the original image "Zelda" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
图6是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的原始图像“Peppers”。Fig. 6 is the original image "Peppers" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
图7是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像加密方法加密后得到的密文图像。Fig. 7 is a ciphertext image encrypted by using the asymmetric double-image encryption method based on the fractional Fourier domain phase recovery process of the present invention.
图8是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的图像“Zelda”的解密密钥φi,2。Fig. 8 is the decryption key φ i,2 of the image "Zelda" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
图9是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的图像“Zelda”的解密密钥φi,d。Fig. 9 is the decryption key φ i,d of the image "Zelda" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
图10是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的图像”Peppers”的解密密钥φi,2。Fig. 10 is the decryption key φ i,2 of the image "Peppers" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
图11是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的图像”Peppers”的解密密钥φi,d。Fig. 11 is the decryption key φ i,d of the image "Peppers" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
图12是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的图像“Zelda”的解密图像。Fig. 12 is a decrypted image of the image "Zelda" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
图13是采用本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法进行加密的图像“Peppers”的解密图像。Fig. 13 is a decrypted image of the image "Peppers" encrypted by the asymmetric double-image decryption method based on the fractional Fourier domain phase recovery process of the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施方式对本发明进行详细说明。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.
基于分数傅里叶域相位恢复过程的非对称双图像加密方法,包括纯相位提取、相位调制、分数傅里叶变换;具体步骤如下:An asymmetric dual-image encryption method based on the phase recovery process in the fractional Fourier domain, including pure phase extraction, phase modulation, and fractional Fourier transform; the specific steps are as follows:
第一步,纯相位提取:有两幅原始灰度图像,使用分数傅里叶域相位恢复过程提取第i(i=1,2)幅灰度图像fi(i=1,2)的纯相位函数ξi,1(i=1,2);在使用分数傅里叶域相位恢复过程提取原始灰度图像fi(i=1,2)的纯相位函数过程中,伴随产生相位模板函数φi,1,φi,2,ξi,2(i=1,2);The first step, pure phase extraction: there are two original grayscale images, use the fractional Fourier domain phase recovery process to extract the pure phase of the i (i=1,2) grayscale image fi ( i =1,2) Phase function ξ i,1 (i=1,2); in the process of extracting the pure phase function of the original grayscale image f i (i=1,2) using the fractional Fourier domain phase recovery process, the phase template function is concomitantly generated φ i,1 ,φ i,2 ,ξ i,2 (i=1,2);
第二步,相位调制:在临时图像生成模块中,一个复矩阵Hi(i=1,2)通过振幅图像g与相应的两个相位函数ξi,1,ξi,2产生The second step, phase modulation: in the temporary image generation module, a complex matrix H i (i=1,2) is generated through the amplitude image g and the corresponding two phase functions ξ i,1 , ξ i,2
Hi=Fβ2{Fβ1[gexp(jξi,1)]exp(jξi,2)} (1)H i =F β2 {F β1 [gexp(jξ i,1 )]exp(jξ i,2 )} (1)
进行相位调制,两个Hi通过卷积运算被组合进一个矩阵HFor phase modulation, two H i are combined into a matrix H by convolution operation
H=H1*H2 (2)H=H 1 *H 2 (2)
式(1)、(2)中j为虚部符号,exp{·}为指数运算,g为相位图像,Fα表示分数傅里叶变换,ξi,1、ξi,2是相位函数,H为调制结果,*表示卷积运算;In formulas (1) and (2), j is the symbol of the imaginary part, exp{ } is the exponential operation, g is the phase image, F α is the fractional Fourier transform, ξ i,1 and ξ i,2 are the phase functions, H is the modulation result, * means the convolution operation;
第三步,分数傅里叶变换:对第二步得到的调制结果H实施α3阶分数傅里叶变换得到计算矩阵的振幅|即为密文Cfinal,解密密钥φi,d也被同时生成:The third step, fractional Fourier transform: implement α 3rd order fractional Fourier transform on the modulation result H obtained in the second step to obtain calculate the amplitude of the matrix | That is, the ciphertext C final , and the decryption key φ i,d is also generated at the same time:
其中,|H|表示组合矩阵的振幅,j为虚部符号,exp{·}为指数运算,arg{·}表示矩阵的相位。Among them, |H| represents the amplitude of the combined matrix, j is the symbol of the imaginary part, exp{·} is the exponent operation, and arg{·} represents the phase of the matrix.
分数傅里叶域相位恢复过程使用三个相位模版函数,φi,1,φi,2,ξi,1,(i=1,2)即为该过程的三个相位模版函数。The fractional Fourier domain phase recovery process uses three phase template functions, φ i,1 ,φ i,2 ,ξ i,1 , (i=1,2) are the three phase template functions of the process.
上述加密方法的解密过程具体为,将最终密文Cfinal和乘上相位函数exp(jφi,d)生成复矩阵对实施-(α2+α3)阶逆分数傅里叶变换得到调制后的结果Hi,由Hi和相位矩阵exp(jφi,2)相乘得到hi,对hi实施-α1阶逆分数傅里叶变换得到然后提取的振幅作为解密图像fi,即:The decryption process of the above encryption method is specifically to multiply the final ciphertext C final by the phase function exp(jφ i,d ) to generate a complex matrix right Implement the -(α 2 +α 3 ) order inverse fractional Fourier transform to obtain the modulated result H i , multiply H i and the phase matrix exp(jφ i,2 ) to obtain h i , implement -α 1 on h i Order inverse fractional Fourier transform to get then extract The amplitude of the decrypted image f i , namely:
fi=|F-α1{F-(α2+α3)[Cfinalexp(jφi,d)]}expj(φi,2)| (4)f i =|F -α1 {F -(α2+α3) [C final exp(jφ i,d )]}expj(φ i,2 )| (4)
本发明加密方法的工作原理是:首先,使用基于分数傅里叶域相位恢复过程的非对称双图像加密方法提取两幅原始灰度图像中每幅图像的纯相位函数。然后,利用卷积运算将两幅图像整合到一幅图像中。最后,对调制得到的结果实施一次α3阶分数傅里叶变换,提取变换后结果的振幅得到最终密文。同时,在加密过程中解密密钥也一并产生。The working principle of the encryption method of the present invention is as follows: firstly, an asymmetric double-image encryption method based on a fractional Fourier domain phase recovery process is used to extract the pure phase function of each image in two original grayscale images. Then, the two images are combined into one image using convolution operation. Finally, perform a α 3rd -order fractional Fourier transform on the modulated result, and extract the amplitude of the transformed result to obtain the final ciphertext. At the same time, the decryption key is also generated during the encryption process.
本发明加密方法原理参见图1,(xi,yi)与(xo,yo)分别表示输入及输出坐标。并且变换核心如下:Refer to Fig. 1 for the principle of the encryption method of the present invention, where ( xi , y i ) and (x o , y o ) denote input and output coordinates, respectively. And transform the core as follows:
K(xi,yi;xo,yo)=Aφexp{iπ[(xi 2+yi 2+xo 2+yo 2)cotφα-2(xixo+yiyo)cscφα]}K(x i ,y i ; x o ,y o )=A φ exp{iπ[(x i 2 +y i 2 +x o 2 +y o 2 )cotφ α -2(x i x o +y i y o )cscφ α ]}
(5)(5)
φα=απ/2 (7)φ α = απ/2 (7)
本发明加密过程参见图2,首先,提取两幅原始灰度图像每幅图像的纯相位函数。具体过程:使用分数傅里叶域相位恢复过程提取第i幅灰度图像fi的纯相位函数ξi,1,φi,1,φi,2,ξi,2为提取第i幅原始灰度图像的纯相位函数过程中伴随产生的相位模板函数,其中i=1,2。α1,α2,α3,β1,β2为迭代相位恢复过程的分数指数。其次,对得到的两个Hi(i=1,2),利用卷积运算计算H。接着,将有关分数指数α1,α2,α3,β1,β2设定好。对第二步得到的结果H实施α3阶分数傅里叶变换得到计算矩阵的振幅即为密文Cfinal,解密密钥φi,d根据公式也被同时生成。Referring to Fig. 2 for the encryption process of the present invention, firstly, the pure phase function of each of the two original grayscale images is extracted. The specific process: use the fractional Fourier domain phase recovery process to extract the pure phase function ξ i,1 of the i-th grayscale image f i , φ i,1 , φ i,2 , ξ i,2 are to extract the i-th original The phase template function concomitantly generated during the pure phase function process of the grayscale image, where i=1,2. α 1 , α 2 , α 3 , β 1 , β 2 are the fractional indices of the iterative phase recovery process. Secondly, for the obtained two H i (i=1, 2), calculate H by convolution operation. Next, the relevant fractional indices α 1 , α 2 , α 3 , β 1 , β 2 are set. Implement α 3rd order fractional Fourier transform on the result H obtained in the second step to get Calculate the amplitude of the matrix That is, the ciphertext C final , and the decryption key φ i,d is also generated simultaneously according to the formula.
解密是加密的逆过程。本发明的解密过程参见图3,具体为,将最终密文Cfinal和乘上相位函数exp(jφi,d)生成复矩阵对实施-(α2+α3)阶逆分数傅里叶变换得到调制后的结果Hi,由Hi和相位矩阵exp(jφi,2)相乘得到hi,对hi实施-α1阶逆分数傅里叶变换得到然后提取的振幅作为解密图像fi,Decryption is the reverse process of encryption. Referring to Fig. 3 for the decryption process of the present invention, specifically, the final ciphertext C final is multiplied by the phase function exp(jφ i,d ) to generate a complex matrix right Implement the -(α 2 +α 3 ) order inverse fractional Fourier transform to obtain the modulated result H i , multiply H i and the phase matrix exp(jφ i,2 ) to obtain h i , implement -α 1 on h i Order inverse fractional Fourier transform to get then extract The amplitude of the decrypted image f i ,
fi=|F-α1{F-(α2+α3)[Cfinalexp(jφi,d)]}expj(φi,2)| (4)f i =|F -α1 {F -(α2+α3) [C final exp(jφ i,d )]}expj(φ i,2 )| (4)
图4为本发明基于分数傅里叶域相位恢复过程的非对称双图像解密方法所用装置的结构示意图。该装置类似于DRPE的4f成像系统,包括两个空间光调制器和两个透镜,两个空间光调制器和两个透镜间隔排列。本发明实施例中,两个空间光调制器为空间光调制器PM1和空间光调制器PM2,两个透镜为透镜L1和透镜L2。透镜L1设置在空间光调制器PM1和空间光调制器PM2之间,透镜L2设置在空间光调制器PM2于解密图像之间,PM1和PM2与电子控制器连接,电子控制器通过计算机与图像传感器CCD连接。将PM1与PM2分别设置为exp(jφi,d)和exp(jφi,2),解密过程以密文图像Cfinal作为入射光输入,使用空间光调制器PM1调制密文图像Cfinal,调制的图像透过透镜L1实现-(α2+α3)阶分数傅里叶变换;使用空间光调制器PM2调制-(α2+α3)阶分数傅里叶变换的结果,调制后的图像透过透镜L2实现-α1阶分数傅里叶变换,即可在CCD上获得解密出的明文图像fi。FIG. 4 is a schematic structural diagram of the device used in the asymmetric double-image decryption method based on the phase recovery process in the fractional Fourier domain of the present invention. The device is similar to DRPE's 4f imaging system, including two spatial light modulators and two lenses, and the two spatial light modulators and two lenses are arranged at intervals. In the embodiment of the present invention, the two spatial light modulators are a spatial light modulator PM1 and a spatial light modulator PM2, and the two lenses are a lens L1 and a lens L2. The lens L1 is arranged between the spatial light modulator PM1 and the spatial light modulator PM2, the lens L2 is arranged between the spatial light modulator PM2 and the decrypted image, PM1 and PM2 are connected with an electronic controller, and the electronic controller communicates with the image sensor through a computer CCD connection. Set PM1 and PM2 as exp(jφ i,d ) and exp(jφ i,2 ) respectively, the decryption process takes the ciphertext image C final as the incident light input, uses the spatial light modulator PM1 to modulate the ciphertext image C final , and modulates The image of the -(α 2 +α 3 ) order fractional Fourier transform is realized through the lens L1; the spatial light modulator PM2 is used to modulate the result of the -(α 2 +α 3 ) order fractional Fourier transform, and the modulated image Through the lens L2 to realize -α 1st order fractional Fourier transform, the decrypted plaintext image f i can be obtained on the CCD.
上述加密方法也可以用光电混合装置来实现,类似于DRPE的4f成像系统,在加密过程中,只是将PM1与PM2替换成相位掩膜exp(jφi,d)和exp(jφi,2)。The above encryption method can also be implemented with a photoelectric hybrid device, which is similar to the 4f imaging system of DRPE. In the encryption process, only PM1 and PM2 are replaced by phase masks exp(jφ i,d ) and exp(jφ i,2 ) .
在本发明中,用关联系数(CC)或均方差(MSE)作为相位恢复过程迭代结束标准,当CC大于提前预设的一个接近1的值或均方差MSE值小于提前预设的一个接近0的值,则迭代终止,CC及MSE的计算公式如下:In the present invention, the correlation coefficient (CC) or mean square error (MSE) is used as the phase recovery process iteration end criterion, when CC is greater than a preset value close to 1 or the mean square error MSE value is less than a preset value close to 0 value, the iteration terminates, and the calculation formulas of CC and MSE are as follows:
其中,g为明文图像,gk为迭代得到的近似明文图像,M,N分别为明文图像的宽度和高度,E[·]是期望值计算符号。假设最后迭代次数为K,则最佳的相位函数为:Among them, g is the plaintext image, g k is the approximate plaintext image obtained by iteration, M and N are the width and height of the plaintext image respectively, and E[·] is the expected value calculation symbol. Assuming that the last number of iterations is K, the optimal phase function is:
φ1=φ1 K,φ2=φ2 K,ξ1=ξ1 K-1,ξ2=ξ2 K (10)φ 1 =φ 1 K , φ 2 =φ 2 K , ξ 1 =ξ 1 K - 1 , ξ 2 =ξ 2 K (10)
图5、图6中的“Zelda”和”Peppers”的原始图像加密后得到的密文图像如图7所示,密文图像呈现固定的白噪声分布,而且仅含有强度信息,图像无法为非法用户提供任何有价值的信息。可见,本发明加密方法的加密度很高。The ciphertext image obtained after encrypting the original images of "Zelda" and "Peppers" in Figure 5 and Figure 6 is shown in Figure 7. The ciphertext image presents a fixed white noise distribution and only contains intensity information, so the image cannot be illegal Users provide any valuable information. It can be seen that the encryption degree of the encryption method of the present invention is very high.
图像”Zelda”的解密密钥φi,2参见图8,可以看出,解密密钥类似于白噪声分布。The decryption key φ i,2 of the image "Zelda" is shown in Figure 8, and it can be seen that the decryption key is similar to a white noise distribution.
图像”Zelda”的解密密钥φi,d参见图9,可以看出,解密密钥类似于白噪声分布。The decryption key φ i,d of the image "Zelda" is shown in Figure 9, and it can be seen that the decryption key is similar to a white noise distribution.
图像”Peppers”的解密密钥φi,2参见图10,可以看出,解密密钥类似于白噪声分布。The decryption key φ i,2 of the image "Peppers" is shown in Figure 10, and it can be seen that the decryption key is similar to a white noise distribution.
图像”Peppers”的解密密钥φi,d参见图11,可以看出,解密密钥类似于白噪声分布。The decryption key φ i,d of the image "Peppers" is shown in Fig. 11. It can be seen that the decryption key is similar to a white noise distribution.
解密出的图像“Zelda”参见图12,比较图5中原图”Zelda”与解密出的”Zelda”图像,可以看出解密图像与原图像几乎没有误差。See Figure 12 for the decrypted image "Zelda". Comparing the original image "Zelda" and the decrypted "Zelda" image in Figure 5, it can be seen that there is almost no error between the decrypted image and the original image.
解密出的图像“Peppers”参见图13,比较图6中原图”Peppers”与解密出的”Peppers”图像,可以看出解密图像与原图像几乎没有误差。See Figure 13 for the decrypted image "Peppers". Comparing the original image "Peppers" in Figure 6 with the decrypted "Peppers" image, it can be seen that there is almost no error between the decrypted image and the original image.
本发明加密方法解决了现有加密系统密钥空间小的问题,提高了密钥空间。通过统计,对于密钥φi,d,密钥空间约为S1≈116256×256;φi,2的密钥空间约为S1≈6256×256。由于加密系统的密钥空间为S1×S2,因此,本发明具有足以对抗暴力攻击的足够大的密钥空间。The encryption method of the invention solves the problem of small key space in the existing encryption system and improves the key space. According to statistics, for the key φ i,d , the key space is approximately S 1 ≈116 256×256 ; the key space of φ i,2 is approximately S 1 ≈6 256×256 . Since the key space of the encryption system is S 1 ×S 2 , the present invention has a sufficiently large key space against brute force attacks.
本发明加密密钥不同于解密密钥,避免了非对称加密算法加密密钥与解密密钥相同、易受攻击的缺点,提高了安全性。The encryption key of the present invention is different from the decryption key, avoids the disadvantage that the encryption key of the asymmetric encryption algorithm is the same as the decryption key and is easily attacked, and improves the security.
通过攻击测试,证明本发明不仅对于暴力攻击的抵抗力强,而且对于噪声与其他的特定攻击的抵抗力也很强。非法用户无法通过攻击图像获取任何有价值的信息。Through the attack test, it is proved that the present invention not only has strong resistance to brute force attack, but also has strong resistance to noise and other specific attacks. Illegal users cannot obtain any valuable information by attacking images.
本发明解密过程可通过光学方法实现,系统简单,操作方便。The decryption process of the invention can be realized by optical method, the system is simple and the operation is convenient.
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CN108154460A (en) * | 2016-12-05 | 2018-06-12 | 广东精点数据科技股份有限公司 | A kind of New chaotic image encryption method and apparatus based on local sensing thought |
CN108154460B (en) * | 2016-12-05 | 2021-06-22 | 广东精点数据科技股份有限公司 | Chaotic image encryption method and device based on local perception thought |
CN109191538A (en) * | 2018-07-06 | 2019-01-11 | 西安理工大学 | A kind of more image authentication methods of optics based on revolution domain Phase Retrieve Algorithm |
CN109413297A (en) * | 2018-09-07 | 2019-03-01 | 西安理工大学 | Turn round the more resume images of optics based on chaos structure phase exposure mask in domain |
CN109492414A (en) * | 2018-11-07 | 2019-03-19 | 上海师范大学 | More image encryptions and authentication method based on biometric keys |
CN110086953A (en) * | 2019-03-12 | 2019-08-02 | 天津大学 | The color image encrypting method with Gyrator transformation is decomposed based on QR |
CN111581658A (en) * | 2020-05-13 | 2020-08-25 | 中国人民解放军海军航空大学 | Method for encrypting image by adopting bilinear Fourier transform |
CN111581658B (en) * | 2020-05-13 | 2022-05-17 | 中国人民解放军海军航空大学 | A Method of Image Encryption Using Bilinear Fourier Transform |
CN112765624A (en) * | 2021-01-19 | 2021-05-07 | 浙江科技学院 | Authenticatable phase-only hologram generation method based on phase optimization and sparse constraint |
CN112765624B (en) * | 2021-01-19 | 2022-05-27 | 浙江科技学院 | Authenticatable phase-only hologram generation method based on phase optimization and sparse constraint |
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