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Intellectual property protection of multimedia content is essential to the successful deployment of Internet content delivery platforms. There are two general approaches to multimedia copy protection: copy prevention and copy detection. Past experience shows that only copy detection based on mark embedding techniques looks promising. Multimedia fingerprinting means embedding a different buyer-identifying mark in each copy of the multimedia content being sold. Fingerprinting is subject to collusion attacks: a coalition of buyers collude and follow some strategy to mix their copies with the aim of obtaining a mixture from which none of their identifying marks can be retrieved; if their strategy is successful, the colluders can redistribute the mixture with impunity. A construction is presented in this paper to obtain fingerprinting codes for copyright protection which survive any collusion strategy involving up to three buyers (3-security). It is shown that the proposed scheme achieves 3-security with a codeword length dramatically shorter than the one required by the general Boneh-Shaw construction. Thus the proposed fingerprints require much less embedding capacity. Due to their own clandestine nature, collusions tend to involve a small number of buyers, so that there is plenty of use for codes providing cost-effective protection against collusions of size up to three.