Security and privacy are two indispensable topics within information and communication systems. Both rely heavily on the generation of high quality cryptographic parameters. Some parameters, such as keys, have the intrinsic requirement that they must be chosen at random. Others, such as pseudonyms, have the additional requirement of being system-wide unique. Furthermore, in cases where pseudonyms are generated by users themselves, the privacy of the associated identity must be explicitly protected. Currently, several mechanisms exist that provide either randomness and privacy or uniqueness. However, no existing solution satisfies all three requirements while remaining efficient in terms of communication. This book introduces Collision-Free Number Generation. Using this concept, an instance within a system can efficiently generate numbers locally, which are provably system-wide unique, appear to be random and protect the privacy of their generator. Furthermore, approaches are presented that allow a set of instances to jointly generate a secret key which - once reconstructed - is system-wide unique. The reader should be familiar with the basics of security and cryptography.