###### 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. digital elevation model; information security; chaos system; configurational information; configurational entropy 2021 5 March 2021  
image via two stages (i.e., confusion and diffusion). At the confusion stage, the positions of pixels are changed. To enhance security, the pixel values are changed at the diffusion stage. Sometimes, these two stages can be achieved simultaneously. Nevertheless, one may notice that the precision of initial parameters for generating chaotic sequences can influence the encryption performance of a chaotic system. At this point, for a given image, one may ask two questions: (i) Can we employ a metric to help optimize an encryption algorithm based on the chaos system? and (ii) What abilities should such a metric have? To answer these two questions, let us first recall the viewpoint proposed by [PERSON] that it is possible to break many kinds of ciphers using a statistical analysis on the histogram and the correlation of adjacent pixels in the cipher image [3]. From this viewpoint, we know that both the composition (proportions of pixels) and configurational information (spatial structures) of an image should be considered when designing an encryption algorithm and when evaluating its performance. This further suggests that we may need to find metrics for capturing both compositional and configurational information of an image. Some metrics have been developed to evaluate the performance of encryption systems upon an image, e.g., correlation [9], NPCR (Number of Pixels Change Rate) [9; 16], UACI (Unified Average Changing Intensity) [9], histogram [17], and Shannon entropy [18; 19; 20]. Theoretically speaking, these metrics are not good enough for capturing both compositional and configurational information. For example, Shannon entropy is a type of statistical entropy [21] and thus is unable to completely capture the configurational information of an image since its calculation relies on the occurrence probabilities of pixels, not the two-dimensional spatial structures. Three DEMs are shown in Figure 1, where the ones in the middle and right frames are the scrambled results of the one in the left frame. They have different spatial structures, whereas their Shannon entropy values are the same. Additionally, the information content of the multiscale representation of a DEM cannot be well-quantified by these metrics. To bridge the gaps induced by these metrics mentioned above, this study utilizes the configurational entropy (thermodynamic entropy) to encrypt DEM. An encryption algorithm is proposed with the integration of a chaos system and linear prediction and is optimized by leveraging the configurational entropy.