Encryption and Decryption Algorithms for Plain Text and Images using Fractional Calculus [Hardcover]

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.

Introduction.- Synchronization of Chaotic Systems.- Stream cyphers and block cyphers.- Liouvillian Systems and Cryptography.- State Observers and Cryptography.- Fractional systems.- Fractional-order Liouvillian systems and encryption.- Fractional-order robust state observers and encryption.- Secure Communications by using Atangana-Baleanu fractional derivative.- Conclusion.Rafael Mart?nez-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-authorlÃÈ