Proofs of Data Possession/Retrievability (PoDP/PoR) schemes are essential to cloud storage services, since they can increase clients' confidence on the integrity and availability of their data. The majority of PoDP/PoR schemes are constructed from homomorphic linear authentication (HLA) schemes, which decrease the price of communication between the client and the server. In this paper, a new subclass of authentication codes, named ε-authentication codes, is proposed, and a modular construction of HLA schemes from ε-authentication codes is presented. We prove that the security notions of HLA schemes are closely related to the size of the authenticator/tag space and the successful probability of impersonation attacks (with non-zero source states) of the underlying ε-authentication codes. We show that most of HLA schemes used for the PoDP/PoR schemes are instantiations of our modular construction from some ε-authentication codes. Following this line, an algebraic-curves-based ε-authentication code yields a new HLA scheme.