With the emergence of IoT (Internet of things), huge amounts of sensitive data are being processed and transmitted everyday in edge devices with little to no security. Due to their aggressive power management schemes, it is a common and necessary technique to make a back-up of their program states and other necessary data in a non-volatile memory (NVM) before going to sleep or low power mode. However, this memory is often left unprotected as adding robust security measures tends to be expensive for these resource constrained systems. In this paper, we propose a lightweight security system for NVM during low power mode. This security architecture uses the memristor, an emerging nanoscale device which is used to build hardware security primitives like PUF (physical unclonable function) based encryption-decryption, true random number generators (TRNG), and memory integrity checking. A reliability enhancement technique for this PUF is also proposed which shows how this system would work even with less-than-100% reliable PUF responses. Together, with all these techniques, we have established a dual layer security protocol (data encryption+integrity check) which provides reasonable security to an embedded processor while being very lightweight in terms of area, power, and computation time. A complete system design is demonstrated with 65nm CMOS and emerging memristive technology. With this, we have provided a detailed and accurate estimation of resource overhead. Analysis of the security of the whole system is also provided.