Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude- and phase- truncation approach
Introduction
Over the past few decades, securing information using optical methods has drawn attention of scientific community because of parallel processing and multi-dimensional operation capability as compared to the digital methods. Various optical information processing schemes have been developed for security applications. For information security and fraud prevention application, Javidi and Horner [1] gave the basic idea for security verification for passports, credit cards, and many other identity proofs. Apart from verification, double random phase encoding (DRPE) technique reported in 1995 is the basic scheme for optical encryption, which makes use of two statistically independent random phase masks (RPMs) as the security keys to encrypt an input image [2], [3]. However, DRPE scheme requires precise alignment of phase key and further needs to generate conjugate of the phase key for successful decryption. Thus, to overcome the drawbacks of generation of conjugate of the phase key in DRPE, Nomura and Javidi [4] proposed a technique for optical encryption based on the joint transform correlator (JTC) architecture. Abookasis et al. [5] proposed an improved optical security system based on two phase-only computer-generated masks using JTC. Islam and Alam [6] proposed a two-channel shifted-phase encoded JTC in order to retrieve a good quality of decrypted image. Rueda et al. [7] introduced a digital holographic configuration in JTC scheme. They also proved that the modification in the diffuser of JTC allows optical multiplexing by means of diffuser lateral shift [8]. Barrera et al. [9] demonstrated a technique to encrypt a movie employing JTC architecture. Rajput and Nishchal [10] used additional encryption keys to increase the security level of non-conventional JTC. Islam et al. [11] proposed a method that employs orthogonal codes for encoding and multiplexing purpose with multiple phase-shifted reference-based optical JTC system for encryption. Barrera et al. [12] gave a multiplexing procedure to encrypt a keyboard in order to use it as a typewriter.
In order to determine the security of the encryption scheme it is beneficial to test them under various attacks. It has been found in Refs. [13], [14] that JTC scheme is vulnerable to known-plaintext attack. Barrera et al. [15] and Qin et al. [16] showed that optical encryption method based on JTC architecture is vulnerable to chosen-plaintext attack. Vilardy et al. [17] proposed a method based on nonlinearity to decrypt a good quality of input image and resist the chosen-plaintext attack.
In the literature, most of the optical image encryption schemes belong to the class of symmetric cryptosystems, in which keys used for encryption, are identical to the decryption keys. Hence, linearity makes the cryptosystem insecure [18], [19], [20], [21], [22], [23], [24], [25]. The symmetric cryptosystem suffers from problems, such as, in key distribution, management, and delivery [26]. To overcome these issues, asymmetric cryptosystem has been proposed [27], [28], [29], [30], [31], [32], [33]. Asymmetric cryptosystem due to its nonlinear behavior makes the encryption system more strong. Recently, a special attack on phase truncation based encryption has been proposed [34]. Further, to avoid this attack new schemes have been developed [35]. This attack is valid if encryption keys are considered as public keys. Recently, collision attack on asymmetric cryptosystem was also proposed [36]. Thus, in order to solve the problem of linearity of DRPE, asymmetric cryptosystem is the desired option.
In this scheme, for the first time we combine the concept of asymmetric cryptosystem with the JTC for security enhancement and introducing non-linearity. An input image is first encrypted using two RPMs in basic JTC architecture and the obtained joint power spectrum (JPS) is further encrypted using phase-truncated Fourier transform approach. To encrypt the JPS, two more RPMs are used, which generate two decryption (asymmetric) keys. For decryption, knowledge of the correct decryption keys is necessary, which yields the JPS and hence the original image is retrieved successfully. The proposed scheme makes the encryption system strong. Qin et al. [16] showed that JTC encryption system is vulnerable to chosen-plaintext attack. Recently, Wang and Zhao [34] demonstrated that asymmetric cryptosystem is also vulnerable to specific attack. In this paper, we prove through the cryptanalysis that the proposed scheme is resistant to a novel hybrid attack, which is the combination of specific attack and chosen-plain text attack. Computer simulation results validate the proposed method.
Section snippets
Encryption scheme
Let f(x,y) be a real image to be encrypted. Fig. 1 shows the optical encryption scheme based on JTC architecture. In the encryption process, RPM given as r1(x,y) is bonded with plain image f(x,y) and is placed at coordinate x=−a of the JTC input plane. On the other half, i.e. x=a, other RPM, r2(x,y) is placed. The JPS which is recorded as ciphertext is given as
Here FT(.) represents the Fourier transformation, (x,y) and (u,v) are coordinates of the input
Decryption scheme
For decryption, as shown in Fig. 1(c) the key obtained in the output domain, k2(ψ,Φ), is bonded with the cipher-text, H(ψ,Φ), and its inverse FT is obtained. The obtained spectrum is phase-truncated as
Now, H1(ξ,η) is bonded with the decryption key, k1(ξ,η), and its inverse FT is again obtained. The obtained spectrum is again phase-truncated, which retrieves the JPS as
Thus we find that after using the correct decryption keys JPS is
Attack analysis
In order to prove that a JTC architecture is resistant against chosen-plaintext attack, we first discuss an specific attack on the encrypted information, H(ψ,Φ) in Section 4.1. It has already been shown in Ref. [34] that an asymmetric cryptosystem based on the phase-truncated Fourier transform approach is vulnerable to the specific attack. Thus, due to specific attack on encrypted information, H(ψ,Φ), the JPS is retrieved. It is also known that the decrypted image obtained through an specific
Simulation results
The simulation study was carried out using MATLAB 2010(b). Fig. 2(a) shows the input image ‘OPTICS LAB IITP’ of size 128×128 pixels placed in a matrix of size 512×512 pixels through zero padding. Fig. 2(b) shows the obtained JPS by Fourier transforming the input plane containing object and keys. The encrypted JPS obtained after using amplitude-, and phase- truncation approach has been shown in Fig. 2(c). The decryption keys, k1(ξ,η) and k2(ψ,Φ) numerically generated has been shown in Fig. 2(d)
Conclusion
In summary, we proposed a novel and highly secure encryption scheme based on JTC architecture combined with amplitude-, and phase- truncation approach. Due to amplitude- and phase- truncation, the encryption scheme becomes asymmetric. Making a JTC based encryption scheme asymmetric enhances the security. Cryptanalysis of the scheme reveals that it is resistant to hybrid attack, which is the combination of specific attack on asymmetric cryptosystem and chosen-plaintext attack on JTC based
Acknowledgment
The authors acknowledge the funding from the Council of Scientific and Industrial Research, Government of India, under Grant no. 03/(1183)/10/EMR-II.
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2020, Optics and Laser TechnologyCitation Excerpt :In the JTC-based cryptosystem [21], the plaintext bonded with a RPM is placed side by side with the encryption key in the input plane and the intensity distribution of the joint power spectrum (JPS) as the encrypted data can be recorded using a common power-law sensor, such as a charge-coupled device (CCD). Consequently, various encryption schemes based on JTC [22–28] have been proposed. On the other hand, various authentication schemes based on optical techniques have also been proposed [29–34].