An effective attack against fingerprints for multimedia is collusion, where several differently marked copies of the same content are averaged or combined to disrupt the underlying fingerprint. In this paper, we investigate the problem of designing fingerprints that can withstand collusion and allow for the identification of colluders. We begin by introducing the collusion problem for additive embedding, and introduce an efficient detection algorithm for orthogonal modulation that identifies the fingerprints associated with K colluders and requires O(K log(n/K)) correlations for a group of n users. We present a construction of collusion-resistant fingerprints based upon anti-collusion codes (ACC) and binary code modulation. Using ACC, we build fingerprints that identify groups of K or less colluders. We present a construction of binary-valued ACC under the logical AND operation using the theory of combinatorial designs. Our code construction requires only O(sqrt{n}) orthogonal signals to accommodate n users. We demonstrate the performance of our ACC for fingerprinting multimedia and identifying colluders through experiments using Gaussian signals.