This book presents the research done by the author during 2003-2007 and is essentially a shortened version of his PhD dissertation titled "New Paradigms in Group-Oriented Cryptography: Non-Interactive Key Agreement, Chain Signatures and Additive Proofs of Knowledge." The thesis had three main contributions: (1) A construction of a black-box Group with Infeasible Inversion, (2) The concept of Chain Signatures, and (3) The notion of Additive Proofs of Knowledge.