Security-enhanced interference-based optical image encryption
Introduction
With the rapid development of computer and internet technologies, unauthorized information usage and distribution become a serious problem, which results in a stringent demand of various encryption techniques. In recent years, optical encryption technique [1] is considered as an important research topic for information security. Optical image encryption has attracted more and more attention due to its marked advantages, such as parallel processing and multiple-parameter characteristic. Since double random phase encoding [1] was proposed, various algorithms and infrastructures [2], [3], [4], [5], [6], [7], [8], [9], such as virtual optics [2], [3], digital holography [4], polarization [5], Fresnel transform [6], gyrator transform [7] and fractional Fourier transform (FrFT) [8], [9], have been further developed in order to enhance cryptosystem security. However, it was found that some cryptosystems could not effectively endure the attacks [10], [11], [12], [13], such as known-plaintext attack [11]. Optical asymmetric cryptosystems, such as phase-truncated Fourier transform [14], have been proposed to resolve the problem inherent in conventional symmetric cryptosystems. In addition, it is also found that when diffractive imaging [15], [16], [17] is applied in optical image encryption, the attack algorithms cannot work.
In recent years, the phase retrieval algorithm [18], [19], [20] is considered as one of the most important technologies for optical image encryption. Wang et al. [18] and Li et al. [19] first proposed phase retrieval algorithm which can iteratively encrypt the plaintext into two phase-only masks (i.e., one mask fixed and another mask extracted). Subsequently, Chang et al. [20] developed phase retrieval algorithm which can embed the plaintext into multiple phase-only masks. The phase-only masks generated are stored or transmitted to the authorized receivers, and either a digital or optical approach can be applied during image decryption. However, an iterative operation is usually required for extracting the phase-only masks during image encryption. Recently, Zhang and Wang [21] proposed a phase retrieval algorithm based on interference principle for optical image encryption. It was illustrated [21] that iterative operations can be avoided during image encryption, and interference strategy could be easily implemented during image decryption. However, there is a silhouette problem in the conventional interference-based optical encryption [22], [23]. Some algorithms [22], [23], such as exchanging strategy [22] and jigsaw transform [23], have been proposed to remove the silhouette. In addition to the silhouette problem, higher security is always desirable for interference-based optical image encryption [21].
In this paper, we propose a novel method to enhance the security for conventional interference-based optical image encryption. A series of fixed phase-only masks (i.e., principal security keys) is used in the optical paths, and interference principle is applied to extract two phase-only masks (i.e., ciphertexts) during image encryption. Since a series of random and fixed phase-only masks is applied as principal security keys, more key space is generated and higher security can be achieved in the proposed optical cryptosystem compared with conventional interference-based optical encryption method [21].
Section snippets
Theoretical analysis
The optical encryption scheme based on interference [21], [22], [23], [24], [25], [26], [27] is briefly summarized. Fig. 1 shows a schematic setup for interference-based optical image encryption in the FrFT domain. To obtain the input image (i.e., plaintext) in the image plane, a digital approach is used to encrypt the plaintext into two phase-only masks, i.e., M1 and M2. In this study, FrFT function orders are the same at the corresponding propagation intervals in the two optical paths. When a
Results and discussion
A numerical experiment shown in Fig. 2 is conducted to demonstrate feasibility and effectiveness of the proposed method. The light wavelength is 632.8 nm, and function orders α1 (or β1) and α2 (or β2) are 0.3 and 0.5, respectively. Pixel size of CCD camera is 4.65 μm, and pixel number is 512×512. The fixed phase-only mask PM_1 is randomly distributed in the range of [0,2π], which can be considered as principal security key. Fig. 3(a) shows an original input image or the plaintext (Baboon with
Concluding remarks
We have proposed a novel method to enhance the security for conventional interference-based optical image encryption in the FrFT domain. A series of fixed and random phase-only masks is used as principal security keys, and subsequently interference principle is applied to extract two phase-only masks M1 and M2 (i.e., the ciphertexts). The results demonstrate that the proposed method is simple and effective. It is also illustrated that security of conventional interference-based optical
Acknowledgment
This work was supported by the Singapore Temasek Defence Systems Institute under Grant TDSI/11–009/1A.
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