Today digital transaction watermarking is a widely accepted mechanism in multimedia security. Copies of one work are distributed with individual watermarks. One major threat on transaction watermarking are collusion attacks. Multiple individualized copies of the work are mixed to produce a counterfeited or undetectable watermark. As a countermeasure so-called collusion secure fingerprint codes have been introduced. These are mathematical codes resistant against collusion attacks, even allowing to identify the attackers involved. The important challenge is to provide fingerprints which are highly reliable and, at the same time, sufficiently compact to be embedded as a watermark according to the payload limit. Approaches that generate probabilistic codewords provide theoretical results for t he average fingerprint. Though, in practice, false alarms only occur at by chance disadvantageously generated fingerprints. This work shows how a correlated generation process can manage these disadvantageously generated fingerprints so as to bound the number of false alarms. This allows us to generate shorter fingerprints while keeping the same security level
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