I am interested in the mathematical theory of chaos, and its applicability to solve problems related to computer security and biology. To do this, I study the topological behaviour of discrete dynamic systems, such as chaotic iterations. The aim is to measure the quality of the unpredictability of such systems, and to quantify it with mathematical proofs. The final challenge is twofold. On the one hand, improve the security of cryptological schemes, such as steganography and digital watermarking, hash functions, the generation of cryptographically secure pseudo-random numbers, and improve security within sensor networks. On the other hand, to study the unpredictable behaviour of phenomena occurring in nature.