In the era of Big Data and Internet of Things (IoT), information security has emerged as an essential system and application metric. The information exchange among the ubiquitously connected smart electronic devices requires functioning reliably in harsh environments, which highlights the need for securing the hardware root of trust. In this work, by leveraging the uniform nonlinear resistive switching of emerging electroforming-free analog memristive device based on BiFeO3 (BFO) thin film, the security-oriented hardware primitive (SoHP) system is developed and optimized with high-security level. The SoHP system utilizes the distinguishable power conversion efficiency generated at second and higher harmonics in low resistance state (memristor with diodelike behavior) and high resistance state (memristor with high resistive behavior) of memristive devices. By exploring the significant influence of writing bias and operational frequency in sourcing input voltage on the dynamic switching behavior of memristive device, the novel 2-memristor encoding scheme and 1-memristor decoding scheme are developed for SoHP system, which realizes a frequency enhancement of 4000 times in comparison to 1-memristor encoding scheme and 2-memristor decoding scheme. The encoded data bits that generated from physically implemented SoHP system pass diverse statistical test suites (i.e. ENT, BSI, and NIST SP-800.22 statistical test suites), which indicates the high randomness distribution of the encoded data and the high-security level of the proposed memristive encoding system.