Many electronic components can be combined into a single chip using VLSI technology. However, as Moore predicted, this technology will soon reach a limit, making it impossible to reduce the size of VLSI circuits further. Scientists are focusing on developing nanotechnology as a result of the impending technological roadblock. Memristor technology presents itself as a viable substitute for transistor-based technology with the advantages of significantly higher speed, reduced dimensions, and low power consumption. This chapter studies the possibility of insertion of Hardware Trojan in a cryptography circuit developed from symmetric functions. Active and passive Trojans are inserted, and their effects on the actual result are analyzed to propose methods for detecting them.