Plaintext related image hybrid encryption scheme using algebraic interpolation and generalized chaotic map

  • Xikun LiangEmail author
  • Xiao Tan
  • Limin Tao


In this paper, a plaintext related image hybrid encryption scheme is proposed based on Lagrange interpolation, generalized Henon map and nonlinear operations of matrices. The proposed scheme consists of three parts. In the first part, a generalized chaotic map is constructed on the basis of Henon map. Using the novel map, a chaotic sequence is built. And then, both the chaotic sequence and the plaintext pixels are used to implement the first nonlinear operation for generating the first cipher matrix associated with the plaintext. By performing an exclusive XOR operation between the original pixels matrix and the first cipher matrix, the diffusion encryption is carried out. In the second part, Lagrange interpolation is used to create the second cipher matrix related to the diffused image; the second nonlinear transformation is developed between the diffused image and the second cipher matrix; and sequence rearrangement is adopted to scramble the diffused image. In the third part, the third nonlinear transformation of matrices based on point operation and rounding operation is implemented on the scrambled image to complete the image encryption. Accordingly, the decryption process is executed by the inverse operations in the opposite order. The proposed algorithm has some distinctive features: a variety of nonlinear tools such as nonlinear polynomial interpolation, nonlinear chaotic map, and nonlinear operations were involved in the scheme. The cryptosystem is designed with the plaintext to enhance the algorithm security. Due to the combination of multiple nonlinear methods and random factors, the scheme is one time pad, which can withstand multiple types of attacks. The algorithm has a clear structure and a simple calculation, so it is easy to program. In addition, encryption simulation and performance analysis are carried out. The feasibility and effectiveness of the algorithm are verified by the simulated results. The security of the algorithm are proved by the objective indicators such as the running time, key space, statistical properties, key sensitivity, and differential analysis, etc.


Non-linear methods Lagrange interpolation Chaotic map Plaintext related Image encryption 



Without institutional funding, the authors carry out the research on image encryption solely due to personal interest. The authors express their sincere gratitude to those who have provided information and suggestions for this work.

Compliance with ethical standards

Ethical statements

We solemnly declare that all authors are well aware of the academic ethics of the journal of Nonlinear Dynamics and are committed to unconditionally complying with these norms.

We certify that this manuscript is original and has not been published and will not be submitted elsewhere for publication while being considered by the journal of Multimedia Tools and Applications. And the study is not split up into several parts to increase the quantity of submissions and submitted to various journals or to one journal over time. No data have been fabricated or manipulated (including images) to support our conclusions. No data, text, or theories by others are presented as if they were our own.

The submission has been received explicitly from all co-authors. And authors whose names appear on the submission have contributed sufficiently to the scientific work and therefore share collective responsibility and accountability for the results.

The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors. Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information Science and EngineeringHangzhou Normal UniversityHangzhouChina
  2. 2.Hangzhou Institute of Service EngineeringHangzhou Normal UniversityHangzhouChina

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