This book offers an alternative for encrypting and decrypting messages using objects called integer and fractional-order estimators or observers, by means of security codes. The authors first establish the class of observers capable of carrying out this work. Then, the type of observers to treat either the integer or fractional order type and their main characteristics is mentioned. The book also presents an essential property of some systems such as Liouville, which is vital for the encryption and decryption of messages in integer and fractional order nonlinear systems by using the synchronization property of chaotic systems. Finally, it addresses some logistic maps such as Mandelbrot sets including Julia and fractal sets, taking advantage of their characteristics to encrypt or recover messages.

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Rafael Martínez-Guerra obtained his B.Sc. degree in Physics and Mathematics at the National Polytechnic Institute (IPN), Mexico City, he holds a M.Sc. degree in Automatic Control of the CINVESTAV-IPN (Center for Research and Advanced Studies of IPN), Mexico City, he holds a M.Sc. degree in Mathematics and Automatic at Ecole des Mines, Paris France and finally, he earned his Ph.D. Degree from Universidad Autonoma Metropolitana in 1996. Currently, he is a researcher at the Automatic Control Department of the CINVESTAV-IPN and a member of the National System Researchers since 1992 (Level 3, currently). He is the author and co-author of more than 90 papers in International Journals and more than 140 contributions to International Conferences in Proceedings. He is co-author of 9 books (7 Springer). His main research interest is in the areas of Nonlinear Systems, Differential Geometric and Differential-Algebraic Methods, Fractional Nonlinear Observers, Fractional Fault Detection and Diagnosis, Secure Communications, Fractional Synchronization and Chaos.

Juan Javier Montesinos-García received a B.S. degree in mechatronics from Papaloapan University, Oaxaca, Mexico in 2014. He received his M. Sc. and Ph.D. degrees in automatic control from CINVESTAV, Mexico City, Mexico in 2015 and 2019, respectively. Currently, he is a postdoctoral researcher at the Technological University of Mixteca (UTM). His current research areas of interest include robust state observers, control of fractional-order systems and secure communications. Juan Pablo Flores-Flores obtained his B.Sc. degree as an aerospace engineer at the National Polytechnic Institute (IPN). He holds a M.Sc. degree in Control Theory from the Automatic Control Department of CINVESTAV-IPN (Center for Research and Advanced Studies of IPN), as well as a Ph.D. from the same institution, which earned in 2022. His main research interests are Nonlinear Systems, Nonlinear Observers, Parameter Identification, Distributed Parameter systems and Synchronization of Integer and Fractional Order Systems.