Digital fingerprinting is a technique for identifyingusers who might try to use multimedia content for unintendedpurposes, such as redistribution. These fingerprints are typicallyembedded into the content using watermarking techniques that aredesigned to be robust to a variety of attacks. A cost-effectiveattack against such digital fingerprints is collusion, whereseveral differently marked copies of the same content are combinedto disrupt the underlying fingerprints. In this paper, weinvestigate the problem of designing fingerprints that canwithstand collusion and allow for the identification of colluders.We begin by introducing the collusion problem for additiveembedding. We then study the effect that averaging collusion hasupon orthogonal modulation. We introduce an efficient detectionalgorithm for identifying the fingerprints associated with Kcolluders that requires O(K log(n/K)) correlations for agroup of n users. We next develop a fingerprinting scheme basedupon code modulation that does not require as many basis signalsas orthogonal modulation. We propose a new class of codes, calledanti-collusion codes (ACC), which have the property that thecomposition of any subset of K or fewer codevectors is unique.Using this property, we can therefore identify groups of K orfewer colluders. We present a construction of binary-valued ACCunder the logical AND operation that uses the theory ofcombinatorial designs and is suitable for both the on-off keyingand antipodal form of binary code modulation. In order toaccommodate n users, our code construction requires onlyO(sqrt{n}) orthogonal signals for a given number of colluders.We introduce four different detection strategies that can be usedwith our ACC for identifying a suspect set of colluders. Wedemonstrate the performance of our ACC for fingerprintingmultimedia and identifying colluders through experiments usingGaussian signals and real images.