Cryptographic primitives are fundamental building blocks for designing security protocols to achieve confidentiality,authentication, integrity and non-repudiation. It is not toomuch to say that the selection and integration of appropriate cryptographic primitives into the security protocols determines the largest part of the efficiency and energy consumption of the wireless sensor network (WSN). There are a number of surveys on security issues on WSNs, which, however, did not focus on public-key cryptographic primitives in WSNs. In this survey, we provide a deeper understanding of public-key cryptographic primitives in WSNs including identity-based cryptography and discuss their main directions and some open research issues that can be further pursued. We investigate state-of-the-art software implementation results We investigate state-of-the-art software implementation results of public-key cryptographic primitives in terms of execution time, energy consumption and resource occupation on constrained wireless devices choosing popular IEEE 802.15.4-compliant WSN hardware platforms, used in real-life deployments. This survey provides invaluable insights on public-key cryptographic primitives on WSN platforms, and solutions to find tradeoffs between ost, performance and security for designing security protocols in WSNs.