A new method of image encryption is presented that uses the combination of the Logistic map with the Q Fibonacci matrix to improve the security and the randomness of the images. Because the method of encryption consists of two key elements, it may be subdivided into two parts. The first part includes the chaotic map stirring where the pixel positions are reordered using the chaotic features of the Logisctic map. The second part is intensity modulation which is done using the Fibonacci Q matrix. The combination of these two processes provides a high level of confusion and diffusion making the encrypted image immune to many of the cryptographic attacks. To show the performance of the method, test images containing garden, bird, fish, and flower patterns with the sizes \(512 \times 512\) pixels and \(1080 \times 1080\) pixels were used. The results obtained after the experiments show that the scheme typographically encrypts the original image while ensuring the correct bits may be extracted for decoding within the embedded image. The encrypted and decrypted images also show that the proposed approach is very effective in securing the sensitive information while at the same time preserving the integrity of the data. The method can be used for secure image transmission and image storage as it guarantees security from unauthorized users.