This paper presents a new method of steganography based on a combination of Catalan objects and Voronoi–Delaunay triangulation. Two segments are described within the proposed method. The first segment describes the process of embedding data and generating a complex stego key. The second segment explains the extraction of a hidden message. The main goal of this paper is to transfer a message via the Internet (or some other medium) using an image so that the image remains absolutely unchanged. In this way, we prevented the potential attacker from noticing some secret message hidden in that picture. Additionally, the complex stego key consists of three completely different parts (the image, the encrypted Delaunay triangulation, and the array Rk in Base64 code), which are very difficult to relate with each other. Finally, a few security analyses of the proposed method are conducted, as well as the corresponding steganalysis.

A method of encryption of the 3D plane in Geographic Information Systems (GIS) is presented. The method is derived using Voronoi-Delaunay triangulation and properties of Catalan numbers. The Voronoi-Delaunay incremental algorithm is presented as one of the most commonly used triangulation techniques for random point selection. In accordance with the multiple applications of Catalan numbers in solving combinatorial problems and their "bit-balanced" characteristic, the process of encrypting and decrypting the coordinates of points using the Lattice Path method (walk on the integer lattice) or LIFO model is given. The triangulation of the plane started using decimal coordinates of a set of given planar points. Afterward, the resulting decimal values of the coordinates are converted to corresponding binary records and the encryption process starts by a random selection of the Catalan key according to the LIFO model. These binary coordinates are again converted into their original decimal values, which enables the process of encrypted triangulation. The original triangulation of the plane can be generated by restarting the triangulation algorithm. Due to its exceptional efficiency in terms of launching programs on various computer architectures and operating systems, Java programming language enables an efficient implementation of our method.

: This paper presents the authentication method using the Delaunay triangulation incremental algorithm and the Catalan objects. The proposed method is a combination of computational geometry and cryptography. This method presents a new step towards encoding the triangle coordinates using the Catalan-key. We provided specific suggestions for the application of this method in the authentication for bank clients by the image encryption. Client authentication verification is performed by asking the client to enter the (x,y) coordinate values of randomly selected indices of an array. If the entered coordinates match the index values in the banking system array, then the transaction or other operation is approved. If the matching fails, it means that we have an unidentified person who has followed the whole process and wants to break into the banking system. There are many advantages arising from a scenario for the user authentication by the assigned Catalan object and the stack permutation method. Also, we provided concrete examples for the Delaunay encryption of image with an authentication scenario and experimental results for the proposed method.

In this paper is presented a procedure for the application of one computational geometry algorithm in the process of generating hidden cryptographic keys from one segment of the 3D image. The presented procedure consists of three phases. In the first phase, is done the separation of one segment from the 3D image and determination of triangulation of the separated polygon. In the second phase, is done a conversion from the obtained triangulation of the polygon in the record which represent the Catalan key. In the third phase, the Catalan-key is applied in encryption of text based on the balanced parentheses combinatorial problem.

This paper present a way of developing web applications for mobile devices in NetBiscuit platform which is implemented at the University of Novi Pazar. The process of implementation is based on project management of e-learning, more precisely on the application of project management (through four phases: definition, planning, management and evaluation). It's designed the combination of project management phase which enables more efficient planning and performing online education with the procedure of design courses for e-learning. The final part contains the process of integration of mobile web applications with Learning Management System (LMS).