Optical cryptosystem scheme for hyperspectral image based on random spiral transform in gyrator domains

Highlights

• An improved random spiral phase transform is introduced for multidimensional image encryption in gyrator domains.

• The proposed algorithm performs well against with various types of attacks.

• Some high sensitive parameters generated during the encryption process will be regarded as the additional keys to enhancing the security of the encryption algorithms.

Abstract

A novel chaotic cryptosystem for hyperspectral image, in this paper, is proposed by using a 4D hyperchaotic system in gyrator transform domains. In encryption process, a random spiral phase function (RSPF) is designed to generate variable spiral phase mask, which can be used for phase encoding with the hyperspectral image. Subsequently, the 4D hyperchaotic system is utilized to generate the chaotic sequences and these chaotic data is employed in designing RSPF, scrambling the hyperspectral image and synthesizing complex ciphertext, respectively. Finally, an improved spiral phase transform (SPT) in gyrator domains is implemented to obtain the ciphertext. To enhance the security of the encryption scheme, the ciphertext is reorganized according to the hyperchaotic attractor. Theoretical simulation analysis is given to demonstrate the validity and robustness of the proposed cryptosystem.

Introduction

In the past decades, the information security technology has attracted more and more attention both in civil and military fields. As the most famous and traditional encryption schemes, the advance encryption standard (AES) and Data encryption standard (DES) are widely used in secret data storage and transmission. However, these traditional encryption algorithm were reported may be vulnerable when resisting some differential cryptanalysis using parallel process and exhaustive attack due to the short key length [1], [2], [1], [2]. Also, the key of AES can be retrieved by some side channel attack in hardware. The highly unpredictable and extremely sensitive to initial conditions feature of the chaotic system are suitable in designing the encryption scheme. Various cryptosystem based on chaotic and hyperchaotic systems have been proposed [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. In these reported encryption algorithm, the nonlinear feature of the chaotic and hyperchaotic data are deeply researched to break the algebraic dependency. In Ref. [11], Zhu proposed an image encryption scheme using improved hyperchaotic sequences. However, Özkaynak and his colleagues report the existing algebraic dependencies and break the encryption scheme using only a few pair of plaintext/ciphertext [12]. Zhao proposed an image encryption scheme based on an improper fractional-order chaotic system and claimed the key length is large enough to against any attacks [13]. Unfortunately, Norouzi soon reported a break method for this encryption algorithm since the keystream is generated independently and the whole algorithm is using the same key, which make it easy to break by employing plaintext attack [14]. Therefore, the issues of algebraic dependencies and key designing are worth paying attention in chaotic based cryptosystem.

In [12], [13], [14], [15], [16], [17], [18], [19], [20], some chaotic-based encryption algorithms in optical transform domains are presented. In fact, some inherent properties of optical information security techniques have significant potential for image encryption [23]. For instance, the properties of fast computing of high parallel processing and multiple complex degrees of freedom processing such as polarization, diffraction, interference, wavelength, amplitude and phase [24]. Optical techniques in information security have been deeply explored soon after the classical double random phase encoding (DRPE) was first proposed by Refregier and Javidi in 1995 [25]. In some of these chaotic-based optical encryption schemes [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], the random data produced by the chaotic system are modulated as the phase mask and placed in the light path to complete the encryption system. To enhance the security of the cryptosystem, some parameters in designing the electro-optical hardware setup or optical transform, such as fractional Fourier transform (FrFT) [19], gyrator transform [20] and Hartley transform [21], are considered as the extra key to protect secret images. Kumar and his colleagues proposed an encryption algorithm using spiral phase transform (SPT) with Fresnel propagations [26]. In [27], an optical color image cryptosystem based on spiral phase transform is reported, in which the chaotic data is utilized to scramble the image pixels. However, to our best knowledge, the spiral phase transform has not been explored in cryptosystem for hyperspectral image. As one of the most important image form, the hyperspectral image has been widely used in geological exploration remote sensing, military target recognition. In the previously presented encryption for hyperspectral image [26], [27], the parameters used for each band of the hyperspectral image are the same or similar one, which make the intact encryption system vulnerable even only one of the bands is cracked by the illegal attacker. The different hyperchaotic data are considered to be employed in different bands of the hyperspectral image to improve the security of the cryptosystem.

In this paper, a novel hyperchaotic-based encryption algorithm in optical gyrator domains is presented. This proposed encryption system protect each band of the hyperspectral image by using different spiral phase function and different keys. The input hyperspectral image is considered as a three-dimensional data having dozens components. Firstly, the independent components of hyperspectral image are modulated with the different spiral phase masks, which generated by RSPF with hyperchaotic data. Simultaneously, the 4D hyperchaotic system is implemented to produce the hyperchaotic sequences. Then part of the chaotic sequences is converted into image format and considered as position matrix for scrambling the two-dimensional image. Finally, an improved spiral phase transform (SPT) in gyrator domains is designed and employed to obtain the ciphertext. In this encryption system, the hyperchaotic data can be regarded as the main keys, the parameters in gyrator transform and RSPF is the additional keys to enhance the security. Various attack experiments are made and discussed to verify the feasibility and robustness of the proposed cryptosystem.

The rest of the paper is arranged in the following sequence. In Section 2, the intact methodology is introduced in detail. In Section 3, various numerical simulation and attack experiments are made to support the capability of the algorithm. In the final section, concluding remarks are summarized.