Smaller, smarter and faster edge devices in the Internet of things era demands secure data analysis and transmission under resource constraints of hardware architecture. Lightweight cryptography on edge hardware is an emerging topic that is essential to ensure data security in near-sensor computing systems such as mobiles, drones, smart cameras, and wearables. In this article, the current state of memristive cryptography is placed in the context of lightweight hardware cryptography. The paper provides a brief overview of the traditional hardware lightweight cryptography and cryptanalysis approaches. The contrast for memristive cryptography with respect to traditional approaches is evident through this article, and need to develop a more concrete approach to developing memristive cryptanalysis to test memristive cryptographic approaches is highlighted.