A Novel Image Encryption Algorithm Based on DNA Subsequence Operation

Algorithm 2

An image decryption algorithm based on DNA subsequence operation.

Input: The decrypted image 𝐵 and chaotic parameters (𝑥₀,𝜇₁,𝛾₁,𝑦₀,𝜇₂,𝛾₂)

Output: The encrypted image 𝐴

(1) [𝐵₁,𝐵₂,𝐵₃,𝐵₄]∶= four DNA sequences obtained from image 𝐵;

(2) [𝐵^′₁,𝐵^′₂,𝐵^′₃,𝐵^′₄]=𝐶𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡(𝐵₁,𝐵₂,𝐵₃,𝐵₄);

(3) [𝑃₁,𝑃₂,𝑃₃,𝑃₄]∶= four groups of DNA subsequences obtained from image [𝐵^′₁,𝐵^′₂,𝐵^′₃,𝐵^′₄];

(4) [𝑥₁,𝑢₁,𝑦₁,𝑢₂,𝑧₁,𝑢₃,𝑞₁,𝑢₄]∶= eight chaotic parameters obtained by 2D Logistic map under chaotic initial parameters (𝑥₀,𝜇₁,𝛾₁,𝑦₀,𝜇₂,𝛾₂);

(5) [𝑋,𝑌,𝑍,𝑄]∶= four chaotic sequences obtained by Logistic map under the chaotic parameters(𝑥₁,𝑢₁,𝑦₁,𝑢₂,𝑧₁,𝑢₃,𝑞₁,𝑢₄);

(6) [𝐸₁,𝐸₂]=𝐸𝑙𝑜𝑛𝑔𝑎𝑡𝑖𝑜𝑛−𝑡𝑟𝑢𝑛𝑐𝑎𝑡𝑖𝑜𝑛(𝑃₁,𝑃₂);

(7) 𝑀₁=𝐼𝑛𝑠𝑒𝑟𝑡𝑖𝑜𝑛(𝐸₁,𝑋);

(8) 𝑀₂=𝐼𝑛𝑠𝑒𝑟𝑡𝑖𝑜𝑛(𝐸₂,𝑌);

(9) 𝐸₃= Transformation (𝑃₃,𝑍);

(10)  𝑀₃=𝐼𝑛𝑠𝑒𝑟𝑡𝑖𝑜𝑛(𝐸₃,𝑍);

(11)  𝐸₄= Transformation (𝐸₄,𝑄);

(12)  𝑀₄=𝑖𝑛𝑠𝑒𝑟𝑡𝑖𝑜𝑛(𝐸₄,𝑄);

(13)  [𝐴₁,𝐴₂,𝐴₃,𝐴₄]=𝑅𝑒𝑐𝑜𝑚𝑏𝑖𝑛𝑒−𝑠𝑢𝑏𝑠𝑒𝑞𝑒𝑛𝑐𝑒(𝑀₁,𝑀₂,𝑀₃,𝑀₄);

(14)  𝐴∶= carry out DNA decoding and recombining binary bit-planes for 𝐴₁,𝐴₂,𝐴₃,𝐴₄;