# Parallel Crossed Chaotic Encryption for Hyperspectral Images
## 1 Introduction  
Nowadays Hyperspectral Images (HI) [1] are an essential tool for many research topics like Remote sensing [2], classification and object recognition [3] and Earth monitoring [4]. HI cameras collect information from across the electromagnetic spectrum retrieving more information than RGB cameras. The HI is a three-dimensional arrange of numbers of size \((n,m,l)\), as is shown in Figure 1, where \(n\) is the numbers of rows, \(m\) the numbers of columns, and \(l\) the number of layers which every layer represents a range of light-waves. In some HI applications, the information contained is sensitive, for example, in military or medical applications; then, it is essential to protect the information. There already exist many various algorithms for secure encrypting [5; 6], like Advanced Encryption Standard (AES) [7; 8; 9; 10] based on irreducible polynomials in Galois fields or the Rivest-Shamir- Adleman (RSA) algorithm [11] based on large prime number factorization. These algorithms offer a secure way to protect sensitive data, and they work with raw data, that is to say, they work at the binary level of data then they can deal with all kind of data structures like images, videos, and documents. However, algorithms like AES and RSA have a high computational cost; consecutively they are not suitable for encrypting a significant amount of data, or for real-time. For this reason, in recent years a new trend of encryption algorithms has been developed specifically for image and video [12]. In [12], we can find the following topics to consider in visual data encryption:  
* **Security**: The required level of security of encrypting passwords or other structured data could differ than the one required for visual data. A more secure algorithm could impact with a high computational cost. * **Speed**: A significant difference between visual data encryption and text-based encryption is that visual data is usually much larger. If we consider a time constraint or real-time execution requirements, the speed of encryption is an important issue. * **Bitstream compliance**: Visual data could have a specific data format. Algorithms for raw data such as AES do not take data format into account and this could cause unexpected crashes in the image decoding. Then, for image encryption algorithms it is highly desirable to obtain a good balance between security and speed. In the last decade, chaotic ciphers [13] have been very used algorithms for image encryption [14]. In [15], a comparison between chaotic and non-chaotic image encryption indicates that chaotic-based schemes are better because of chaos is nonlinear, deterministic and highly sensitive to initial conditions. This conclusion is based on a comparison of a correlation coefficient, information entropy analysis, compression friendliness, maximum derivation, uncertain derivation, avalanche effect, Number of Changing Pixel Rate (NPCR), Unified Average Changed Intensity (UACI) [16], and key space analysis. However, in nowadays chaotic image encryption schemes are specific for gray-scale images or RGB, and there is not an ad hoc encryption algorithm for HI. In the present paper, we propose a new chaotic encryption algorithm for HI which take advantage for designing a fast and high-entropy-valued algorithm. We also introduce the idea of crossed chaotic encryption (CCE), and we empirically show how CCE obtains better entropy results. Finally, we offer a comparison between serial and parallel implementations. The proposed algorithm obtain high-speed results in the parallel version, and high entropy compared with another state of the art algorithms. The paper is structured as follows: In Section 2, we briefly review the basic properties of chaotic systems and chaotic encryption. In Section 3, we develop the idea of crossed chaotic encryption and the proposed scheme for HI. In Section 4, we show the results and comparison, and we also discuss the cryptanalytic features of the proposed algorithm. Finally, in Section 5 the conclusions are shown. Figure 1: Hyperspectral Image.