Almost all of today's security systems rely on cryptographic primitives as core components which are usually considered the most trusted part of the system. The realization of these primitives on the underlying processing platform plays a crucial role for any real-world deployment. In this work, we discuss new trends in public-key cryptography that could potentially establish as alternatives to the currently used RSA and ECC cryptosystems. Analyzing these trends from a developer's perspective, we identify the requirements for optimal processing architectures. Moreover, we investigate if these requirements are already satisfied with latest processing platforms, i.e., which of the streaming, hybrid, multi-core or application-specific instructions processors provide a most promising target architecture.