A Private Information Retrieval (PIR) protocol allows a user to obtain information from a database in a manner that prevents the database from knowing which data was retrieved. Although substantial progress has been made in the discovery of computationally PIR (cPIR) protocols with reduced communication complexity, there has been relatively little work in reducing the computational complexity of cPIR protocols. In particular, Sion and Carbunar argue that existing cPIR protocols are slower than the trivial PIR protocol (in overall performance). In this paper, we present a new family of cPIR protocols with a variety of security and performance properties. Our protocols enable much lower CPU overhead for the database server. When the database is viewed as a bit sequence, only addition operations are performed by the database server. The security of the general version of our protocol depends on either a Hidden Modular Group Order (HMGO) assumption, (a new assumption), or sender anonymity, and we present two specialized protocols, each of which depends on one of the two assumptions, respectively. For our trapdoor group protocol, we assume (the HMGO assumption) that given only the elements be ₁, ..., be _t in the group , where e _i  < m/t and t is small, it is hard to compute the group order m. One version of our cPIR protocol depends only on sender anonymity, which to our knowledge, is the first cPIR protocol to depend only on an anonymity assumption. Our prototype implementation shows that our performance compares favorably with existing cPIR protocols.