Fingerprinting is an essential tool to shun legal buyers of digital content from illegal redistribution. In fingerprinting schemes, the merchant embeds the buyer's identity as a watermark into the content so that the merchant can retrieve the buyer's identity when he encounters a redistributed copy. To prevent the merchant from dishonestly embedding the buyer's identity multiple times, it is essential for the fingerprinting scheme to be anonymous. Kuribayashi and Tanaka, 2005, proposed an anonymous fingerprinting scheme based on a homomorphic additive encryption scheme, which uses basic quantization index modulation (QIM) for embedding. In order, for this scheme, to provide sufficient security to the merchant, the buyer must be unable to remove the fingerprint without significantly degrading the purchased digital content. Unfortunately, QIM watermarks can be removed by simple attacks like amplitude scaling. Furthermore, the embedding positions can be retrieved by a single buyer, allowing for a locally targeted attack. In this paper, we use robust watermarking techniques within the anonymous fingerprinting approach proposed by Kuribayashi and Tanaka. We show that the properties of an additive homomorphic cryptosystem allow for creating anonymous fingerprinting schemes based on distortion compensated QIM (DC-QIM) and rational dither modulation (RDM), improving the robustness of the embedded fingerprints. We evaluate the performance of the proposed anonymous fingerprinting schemes under additive-noise and amplitude-scaling attacks.