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Security and privacy are two indispensable topics withininformation and communication systems. Both rely heavily on thegeneration of high quality cryptographic parameters. Someparameters, such as keys, have the intrinsic requirement that theymust be chosen at random. Others, such as pseudonyms, have theadditional requirement of being system-wide unique. Furthermore, incases where pseudonyms are generated by users themselves, theprivacy of the associated identity must be explicitly protected.Currently, several mechanisms exist that provide either randomnessand privacy or uniqueness. However, no existing solution satisfiesall three requirements while remaining efficient in terms ofcommunication. This book introduces Collision-Free NumberGeneration. Using this concept, an instance within a system canefficiently generate numbers locally, which are provablysystem-wide unique, appear to be random and protect the privacy oftheir generator. Furthermore, approaches are presented that allow aset of instances to jointly generate a secret key which - oncereconstructed - is system-wide unique. The reader should befamiliar with the basics of security and cryptography.