This research proposes a new image encryption scheme based on Lorenz hyperchaotic system and Rivest–Shamir–Adleman (RSA) algorithm. Firstly, the initial values of the Lorenz hyperchaotic system are generated by RSA algorithm, and the key stream is produced iteratively. In order to change the position and gray value of the pixel, the image data are hidden by additive mode diffusion. Secondly, the diffusion image matrix is reshaped into a one-dimensional image matrix, which is confused without repetition to hide the image data again. Then, the finite field diffusion algorithm is executed to realize the third hiding of the image information. In order to diffuse the pixel information into the entire cipher image, the additive mode diffusion algorithm needs to be looped twice. Finally, the cipher image can be obtained. The experimental results prove that the image encryption scheme proposed in this research is effective and has strong antiattack and key sensitivity. Moreover, the security of this encryption scheme relies on the RSA algorithm, which has high security.

In this paper, we mainly discuss the uniqueness problem when an entire function shares 0 CM and nonzero complex constant a IM with its difference operator. We also consider the general case where they share two distinct complex constants a ∗ $a^{*}$ CM and a IM under some additional condition and give some further discussions.

Project Euclid - mathematics and statistics online

We study the uniqueness problems on entire functions and their difference operators or shifts. Our main result is a difference analogue of a result of Jank‐Mues‐Volkmann, which is concerned with the uniqueness of the entire function sharing one finite value with its derivatives. Two relative results are proved, and examples are provided for our results.