Image Encryption and Decryption Using Key Sequence of Triple Logistic Map for Medical Applications

In the present world scenario, security of medical images from unauthorized access is one of the key challenges. This paper provides one of the solutions to solve the security of medical images. The proposed scheme uses a combination of key sequences of Triple Logistic Map (TLM) for the encryption process. To generate the key sequence Logistic function is used with initial value X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and r. The three key sequences{X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> }, {X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2i</sub> and {X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3i</sub> } with different initial value are used (X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> :/ X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> :/ X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">30</sub> ) with r=3.99. The key sequences {X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">li</sub> }` {X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2i</sub> } and {X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3i</sub> } are converted into discrete key sequence {K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">li</sub> }, {K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2i</sub> } and {K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3i</sub> } in the range of 0 to 255. The combined key sequence {K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> } is obtained using bit by bit logical XOR operation between {K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">li</sub> }, {K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2i</sub> }, and {K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3i</sub> }. The resultant Key sequence {Ki} is used forthe encryption process of the medical image. To evaluate the performance of the proposed scheme different grayscale images are chosen. The proposed TLM based image encryption scheme is compared with the encryption scheme using (i) Logistic Map (LM) alone ii) Double Logistic Map (DLM). To evaluate the proposed scheme parameters such as (i) Visual analysis (ii) Histogram plot (iii) Mean Square Error (MSE) iv) Correlation (v) Entropy is used. The simulation result shows that the proposed TLM based scheme provides better performance and immune to statistical attacks.