Encryption of color images using Hadamard matrices

Abstract

There are many methods of encrypting information. Encrypting information using Hadamard matrices is one of the methods that is best for encrypting graphic information or information in the form of images. In this paper, the Hadamard matrices and their classification were investigated, and it was determined that there are four main types of Hadamard matrices: the canonical Hadamard matrices (type C), the "light" Hadamard matrix with a minimum number of elements equal to -1, the Hadamard matrix "50 / 50 "with equal number of elements equal to 1 and -1 (type M), semi-canonical Hadamard matrix (type D). Also their feature and ability to use in the image encryption method were analyzed, as well as the feature with color image encoding. An encryption method that used the Hadamard matrix to encrypt color raster images was identified. In the process, it was determined that it was sufficient to use non-orthogonal Hadamard base matrices, but in the future, 16 Hadamard 4x4 support matrices could be used to improve the crypto-stability of the application. An algorithm for encrypting image pixel combinations using the Hadamard matrices was developed. First, for each pixel of the image, this method randomly determines three Hadamard matrices R, G and B. Then, for each matrix of the encoded image, a matrix key is selected. The key matrix is generated in such a way that when you overlay one matrix on another, they form a combination of four pixels that are as close as possible to the pixel of the input / secret image. The R, G, and B matrices of one pixel of the encoded image and key overlap. The matrix data is then added to the encoded image and key image respectively according to the pixel position. As a result, the web application user receives two images (encoded image and key). Only one of them cannot play a secret image. A web application was developed that uses this encryption method to encode and decode color images.