This paper studies anonymous and confidential genomic case and control computing within the federated framework leveraging SPDZ. Our contribution mainly comprises the following three-fold: \begin{itemize} \item In the first fold, an efficient construction of Beaver triple generators (BTGs) formalized in the 3-party computation leveraging multiplicatively homomorphic key management protocols (mHKMs) is presented and analysed. Interestingly, we are able to show the equivalence between BTGs and mHKMs. We then propose a lightweight construction of BTGs, and show that our construction is secure against semi-honest adversary if the underlying multiplicatively homomorphic encryption is semantically secure. \item In the second fold, a decoupling model for SPDZ with explicit separation of BTGs from MPC servers (MPCs) is introduced and formalized, where BTGs aim to generate the Beaver triples while MPCs to process the input data. A new notion, which we call blind triple dispensation protocol, is then introduced for securely dispensing the generated Beaver triples, and constructed from mHKMs. We demonstrate the power of mHKMs by showing that it is a useful notion not only for generating Beaver triples but also for securely dispensing triples as well. \item In the third-fold, a lightweight genomic case and control computing model is proposed, which reaches the anonymity and confidentiality simultaneously. An efficient truncation algorithm leveraging the depicted BTGs above is then proposed by eliminating computational cost heavy PRandBitL() and PRandInt() protocols involved in the state-of-the-art solutions and thus largely benefits us computing residual vectors for industrial scale deployment.