Block encryption algorithms are now the most widely used cipher systems in the world to protect our communications and our data. Despite the fact that their design is open and public, there is absolutely no guarantee that there do not exist hidden features, at the mathematical design level, that could enable an attacker to break those systems in an operational way. Such features are called backdoors or trapdoors. The present book intends to address the feasibility of a particular class of such backdoors based on partitionning the plaintext and ciphertext message spaces. Going from the theory to the practical aspects, it is shown that mathematical backdoors in encryption systems are possible. This book, thus, intends to initiate a new field of research.