Online/offline signature schemes are useful in many situations, and two such scenarios are considered in this dissertation: bursty server authentication and embedded device authentication. In this dissertation, new techniques for online/offline signing are introduced, those are applied in a variety of ways for creating online/offline signature schemes, and five different online/offline signature schemes that are proved secure under a variety of models and assumptions are proposed. Two of the proposed five schemes have the best offline or best online performance of any currently known technique, and are particularly well-suited for the scenarios that are considered in this dissertation. To determine if the proposed schemes provide the expected practical improvements, a series of experiments were conducted comparing the proposed schemes with each other and with other state-of-the-art schemes in this area, both on a desktop class computer, and under AVR Studio, a simulation platform for an 8-bit processor that is popular for embedded systems. Under AVR Studio, the proposed SGE scheme using a typical key size for the embedded device authentication scenario, can complete the offline phase in about 24 seconds and then produce a signature (the online phase) in 15 milliseconds, which is the best offline performance of any known signature scheme that has been proven secure in the standard model. In the tests on a desktop class computer, the proposed SGS scheme, which has the best online performance and is designed for the bursty server authentication scenario, generated 469,109 signatures per second, and the Schnorr scheme (the next best scheme in terms of online performance) generated only 223,548 signatures. The experimental results demonstrate that the SGE and SGS schemes are the most efficient techniques for embedded device authentication and bursty server authentication, respectively.