When initializing cryptographic systems or running cryptographic protocols, the randomness of critical parameters, like keys or key components, is one of the most crucial aspects. But, randomly chosen parameters come with the intrinsic chance of duplicates, which finally may cause cryptographic systems including RSA, ElGamal and Zero-Knowledge proofs to become insecure. When concerning digital identifiers, we need uniqueness in order to correctly identify a specific action or object.

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... ly we also need randomness here. Without randomness, actions become linkable to each other or to their initiator's digital identity. So ideally the employed (cryptographic) parameters should fulfill two potentially conflicting requirements simultaneously: randomness and uniqueness. This article proposes an efficient mechanism to provide both attributes at the same time without highly constraining the first one and never violating the second one. After defining five requirements on random number generators and discussing related work, we will describe the core concept of the generation mechanism. Subsequently we will prove the postulated properties (security, randomness, uniqueness, efficiency and privacy protection) and present some application scenarios including systemwide unique parameters, cryptographic keys and components, identifiers and digital pseudonyms.