A new DNA coding and hyperchaotic system based asymmetric image encryption algorithm

Min Liu; Guodong Ye; Min Liu; Guodong Ye

doi:10.3934/mbe.2021194

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3887-3906. doi: 10.3934/mbe.2021194

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Research article Special Issues

A new DNA coding and hyperchaotic system based asymmetric image encryption algorithm

Min Liu ,
Guodong Ye ^,

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

Received: 13 March 2021 Accepted: 28 April 2021 Published: 06 May 2021

In this paper, an asymmetric image encryption algorithm based on DNA coding and hyperchaotic system is designed. Unlike other image encryption schemes, for example, sharing of same private keys between sender and receiver, and fixed rules with simple operation, three stages are studied as follows to deal with these problems. Firstly, to eliminate the possible risk of key transmission and management, the initial values of the hyperchaotic system are generated for ahead by the RSA (Rivest-Shamir-Adleman) algorithm and the plain image, in which the sum of odd rows, even rows, odd columns, and even columns are computed respectively to extra the plain message from the plain image as input of RSA algorithm. Then, a mathematical map is established to transform all of them into initial values of the hyperchaotic system. Secondly, the pixel level permutation is performed to confuse the image according to the chaotic sequences generated. Finally, to solve the problem of fixed rules with simple operations in current DNA based image encryption algorithms, dynamical DNA encryption is designed to diffuse the permuted image. The process of DNA encryption includes DNA coding, DNA operation and DNA decoding. In particular, DNA rules are selected according to chaotic sequences dynamically, rather than fixed rules with simple operation. Theoretical analysis and numerical simulations show that the proposed algorithm is secure and reliable for image encryption.
- DNA,
- hyperchaotic system,
- image encryption,
- RSA,
- security
Citation: Min Liu, Guodong Ye. A new DNA coding and hyperchaotic system based asymmetric image encryption algorithm[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3887-3906. doi: 10.3934/mbe.2021194

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Abstract

In this paper, an asymmetric image encryption algorithm based on DNA coding and hyperchaotic system is designed. Unlike other image encryption schemes, for example, sharing of same private keys between sender and receiver, and fixed rules with simple operation, three stages are studied as follows to deal with these problems. Firstly, to eliminate the possible risk of key transmission and management, the initial values of the hyperchaotic system are generated for ahead by the RSA (Rivest-Shamir-Adleman) algorithm and the plain image, in which the sum of odd rows, even rows, odd columns, and even columns are computed respectively to extra the plain message from the plain image as input of RSA algorithm. Then, a mathematical map is established to transform all of them into initial values of the hyperchaotic system. Secondly, the pixel level permutation is performed to confuse the image according to the chaotic sequences generated. Finally, to solve the problem of fixed rules with simple operations in current DNA based image encryption algorithms, dynamical DNA encryption is designed to diffuse the permuted image. The process of DNA encryption includes DNA coding, DNA operation and DNA decoding. In particular, DNA rules are selected according to chaotic sequences dynamically, rather than fixed rules with simple operation. Theoretical analysis and numerical simulations show that the proposed algorithm is secure and reliable for image encryption.

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