Cocks’ identity-based encryption (IBE) scheme is the first IBE scheme that avoids the use of bilinear maps. Based on quadratic residues and due to its simplicity, the scheme gained much attention from researchers. Unfortunately, the scheme is not anonymous in the sense that the cryptotexts may reveal the identities for which they have been computed. Several anonymous variants of it have then been proposed. In this paper we revise Joye’s approach to the anonymization of the Cocks’ IBE scheme. Due to some recent results on the distribution of quadratic residues, we present a very simple and direct approach that leads to Joye’s scheme.