Novel Steganographic Method Based on Hermitian Positive Definite Matrix and Weighted Moore–Penrose Inverses

Abstract

In this paper, we describe the concept of a new data-hiding technique for steganography in RGB images where a secret message is embedded in the blue layer of specific bytes. For increasing security, bytes are chosen randomly using a random square Hermitian positive definite matrix, which is a stego-key. The proposed solution represents a very strong key since the number of variants of positive definite matrices of order 8 is huge. Implementing the proposed steganographic method consists of splitting a color image into its R, G, and B channels and implementing two segments, which take place in several phases. The first segment refers to embedding a secret message in the carrier (image or text) based on the unique absolute elements values of the Hermitian positive definite matrix. The second segment refers to extracting a hidden message based on a stego-key generated based on the Hermitian positive definite matrix elements. The objective of the data-hiding technique using a Hermitian positive definite matrix is to embed confidential or sensitive data within cover media (such as images, audio, or video) securely and imperceptibly; by doing so, the hidden data remain confidential and tamper-resistant while the cover media’s visual or auditory quality is maintained.