Asymmetric image encryption scheme based on the Quantum logistic map and cyclic modulo diffusion

Guodong Ye; Huishan Wu; Kaixin Jiao; Duan Mei; Guodong Ye; Huishan Wu; Kaixin Jiao; Duan Mei

doi:10.3934/mbe.2021275

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 5427-5448. doi: 10.3934/mbe.2021275

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Research article

Asymmetric image encryption scheme based on the Quantum logistic map and cyclic modulo diffusion

Faculty of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China

Academic Editor: Danilo Pelusi

Received: 06 May 2021 Accepted: 15 June 2021 Published: 18 June 2021

In this study, a novel asymmetric image encryption scheme based on the Rivest-Shamir-Adleman (RSA) algorithm and Arnold transformation is proposed. First, the asymmetric public key RSA algorithm is used to generate the initial values for a quantum logistic map. Second, the parameters of the Arnold map are calculated. Then, Arnold scrambling operation is performed on the plain image to achieve the rough hiding of image information. Third, each row and each column of the image are taken as different units respectively and then exclusive-OR (XOR) diffusion is applied. Finally, the generated keystream is used to perform an end-to-start cyclic modulo diffusion operation for all rows and columns to produce the final cipher image. In addition, the keystream is related to the plain image, which can enhance the ability to resist chosen plaintext attack and known plaintext attack. The test results also show that the proposed encryption algorithm has strong plain sensitivity and key sensitivity.
- Quantum logistic map,
- Arnold map,
- image encryption,
- end-to-start cyclic modulo diffusion
Citation: Guodong Ye, Huishan Wu, Kaixin Jiao, Duan Mei. Asymmetric image encryption scheme based on the Quantum logistic map and cyclic modulo diffusion[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 5427-5448. doi: 10.3934/mbe.2021275

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Abstract

In this study, a novel asymmetric image encryption scheme based on the Rivest-Shamir-Adleman (RSA) algorithm and Arnold transformation is proposed. First, the asymmetric public key RSA algorithm is used to generate the initial values for a quantum logistic map. Second, the parameters of the Arnold map are calculated. Then, Arnold scrambling operation is performed on the plain image to achieve the rough hiding of image information. Third, each row and each column of the image are taken as different units respectively and then exclusive-OR (XOR) diffusion is applied. Finally, the generated keystream is used to perform an end-to-start cyclic modulo diffusion operation for all rows and columns to produce the final cipher image. In addition, the keystream is related to the plain image, which can enhance the ability to resist chosen plaintext attack and known plaintext attack. The test results also show that the proposed encryption algorithm has strong plain sensitivity and key sensitivity.

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