Creation of S-box based on a hierarchy of Julia sets: image encryption approach

The newly introduced family of complex chaotic maps has different behavior concerning the well-known complex chaotic maps. These complex maps have excellent properties such as invariant measures and fractal features. The present study introduces a new algorithm that, as a standard format, can be used in cyberspace. To achieve a low automatic correlation, S-box is constructed based on a complex map. Then, an image encryption algorithm based on a designated S-box is proposed. The complex and ergodic nature of the introduced hierarchy proposed the large and safe Keyspace for encryption. Theoretical and experimental results have indicated that the proposed algorithm is high sensitivity to key, and robust to attacks.