A Novel Approach to Data Encryption Based on Matrix Computations

In this paper, we provide a new approach to data encryption using generalized inverses. Encryption is based on the implementation of weighted Moore–Penrose inverse A†MN(nxm) over the nx8 constant matrix. The square Hermitian positive definite matrix N8x8 p is the key. The proposed solution represents a very strong key since the number of different variants of positive definite matrices of order 8 is huge. We have provided NIST (National Institute of Standards and Technology) quality assurance tests for a random generated Hermitian matrix (a total of 10 different tests and additional analysis with approximate entropy and random digression). In the additional testing of the quality of the random matrix generated, we can conclude that the results of our analysis satisfy the defined strict requirements. This proposed MP encryption method can be applied effectively in the encryption and decryption of images in multi-party communications. In the experimental part of this paper, we give a comparison of encryption methods between machine learning methods. Machine learning algorithms could be compared by achieved results of classification concentrating on classes. In a comparative analysis, we give results of classifying of advanced encryption standard (AES) algorithm and proposed encryption method based on Moore–Penrose inverse.