Método Criptográco Baseado em Autômatos Celulares Bidimensionais para Cifragem de Imagens

Abstract

This work proposes a new symmetric-key cryptographical model based on von Neumann two-dimensional, heterogeneous and non-additive cellular automata. The encryption process is performed by calculating consecutive pre-images and decryption process by the forward evolution of cellular automata. The proposed model was based on earlier work which used one-dimensional cellular automata, called Hybrid Cellular Automata (HCA). The inhomogeneity of the automaton, a legacy of HCA, is achieved by using two rules in the process of calculating pre-images. One of the rules is used only in boundary lattice cells to ensure the existence of the preimage, their only function is to perform a shift of the bits. The other rule is chaotic and it is responsible for perform the process of efective scrambling the lattice. The proposition of a new model to encrypt images is justied, because the conventional models of a single dimension are not concerned with spatial characteristics of images. Moreover, cellular automata structures because they are very simple and inherently parallel facilitate the ecient implementation in hardware. Due to the proposed model to use an spacial encryption, the result of cryptography has a higher quality, thus increasing the security of information. The validity and eciency of the model was assessed from multiple tests performed with difierent sets of images and samples of rules with von Neumann neighborhood of radius 1 and radius 2. In the case of rules with a neighborhood radius 1, the full set of keys of 16 bits has been tested thoroughly. The results conrm that the method has the properties of confusion and difiusion. From the results obtained in the tests, it was possible to specify a new cryptographic system which was named Two-Dimensional Hybrid Cellular Automata (THCA). The THCA can be applied in encryption of image or linear texts. When applied to the scrambling of linear texts, the THCA operates with 256-bit keys, blocks of 1024 bits and uses 15 steps of calculating pre-images in encryption. When applied to the encryption of images, the THCA operates with 256-bit keys, and each image is treated with a single block, which is encrypted in a maximum of 25 steps of pre-images, since its binary matrix does not exceed 512 Kbytes and the biggest dimension does not exceed 2048 bits. If it is larger than these dimensions, the image must be broken into blocks of 2048 x 2048 bits, which will be encrypted in 25 steps of pre-images.