Soft Computing

, Volume 23, Issue 16, pp 7045–7053 | Cite as

Image encryption scheme combining a modified Gerchberg–Saxton algorithm with hyper-chaotic system

  • Huiqing Huang
  • Shouzhi YangEmail author
  • Ruisong Ye
Methodologies and Application


We propose a new image encryption algorithm based on a modified Gerchberg–Saxton algorithm and hyper-chaotic system. First, original image is encoded into a phase function by using the modified Gerchberg–Saxton algorithm, which is controlled by hyper-chaotic system. Then, Josephus traversing is employed to scramble the created phase function. Lastly, the scrambled result is confused and diffused by using hyper-chaotic system simultaneously. The numerical simulations verify the validity and reliability of the proposed scheme.


Image encryption Gerchberg–Saxton algorithm Hyper-chaotic system Josephus traversing 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11071152, 11601188, 61403164), the Natural Science Foundation of Guangdong Province (Grant No. 2015A030313443).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShantou UniversityShantouPeople’s Republic of China
  2. 2.School of MathematicsJiaying UniversityMeizhouPeople’s Republic of China

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