Configurational entropy for optimizing the encryption of digital elevation model based on chaos system and linear prediction

Abstract

A digital elevation model (DEM) digitally records information about terrain variations and has found many applications in different fields of geosciences. To protect such digital information, encryption is one technique. Numerous encryption algorithms have been developed and can be used for DEM. A good encryption algorithm should change both the compositional and configurational information of a DEM in the encryption process. However, current methods do not fully take into full consideration pixel structures when measuring the complexity of an encrypted DEM (e.g., using Shannon entropy and correlation). Therefore, this study first proposes that configurational entropy capturing both compositional and configurational information can be used to optimize encryption from the perspective of the Second Law of Thermodynamics. Subsequently, an encryption algorithm based on the integration of the chaos system and linear prediction is designed, where the one with the maximum absolute configurational entropy difference compared to the original DEM is selected. Two experimental DEMs are encrypted for 10 times. The experimental results and security analysis show that the proposed algorithm is effective and that configurational entropy can help optimize the encryption and can provide guidelines for evaluating the encrypted DEM.