Fingerprinting is an essential tool to shun legal buyers of digital content from illegal redistribution. An efficient, anonymous fingerprinting scheme has been proposed by Kuribayashi and Tanaka to provide a secure and efficient protocol for both buyer and merchant . However, the underlying watermarking scheme is based on basic quantization index modulation (QIM). Unfortunately, QIM watermarking is relatively fragile to even the simplest attacks, such as additive noise attacks and amplitude scaling. In order for this fingerprinting scheme to provide sufficient guarantees for the merchant, the buyer must be unable to remove the fingerprint without significantly degrading the purchased digital content. In this paper, we use robust watermarking techniques with the anonymous fingerprinting approach proposed by Kuribayashi and Tanaka. In particular, we consider rational dither modulation (RDM). We show that homomorphic properties of the Okamoto-Uchiyama cryptosystem also allow for creating an anonymous fingerprinting scheme based on RDM.