In this talk I will give a brief survey of my research in the field of cryptography conducted for the past twenty years. The importance of developing discrete mathematical structure suitable for real-life applications in symmetric-key encryption schemes (and cryptography in general) will be motivated on a non-professional level (students will not be bored), thus rather providing a big picture than insisting on unnecessary details related to my scientific work. Some highlights of my research work will be mentioned related to both applicative aspects of discrete mathematical structures, such as the use of Boolean functions to design orthogonal sequences for CDMA applications, and also to purely mathematical context such as the construction of semi-fields and projective/affine spaces. This will lead us to some nice problems (open for more than 20 years) that concern the theory of finite fields or Boolean functions which can be formulated in a compact and elegant way. These problems are exactly the kind of problems that arise our intrigue and give us a motivation to keep on with research. The issue of academic freedom to deal with these »hard« problems will be also briefly addressed.