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Proxy signatures have found extensive use in authenticating agents acting on behalf of users in applications such as grid computing, communications systems, personal digital assistants, information management and e-commerce. Importance of proxy signatures has been repeatedly highlighted by applied cryptographers through different variations, namely threshold proxy signatures, blind proxy signatures and so forth. Unfortunately, most recent constructions of proxy signatures only improve on minor weaknesses of previously built schemes, and most often do not deliver formal security guarantees. In this study, the authors propose a technique to construct provably secure proxy signature schemes using trapdoor hash functions that can be used to authenticate and authorised agents acting on behalf of users in agent-based computing systems. They demonstrate the effectiveness of their approach for creating practical instances by constructing a discrete log-based instantiation of the proposed generic technique that achieves superior performance in terms of verification overhead and signature size compared with existing proxy signature schemes. Formal definitions, security specifications and a detailed theoretical analysis, including correctness, security and performance, of the proposed proxy signature scheme have been provided.