A true random-number generator (TRNG) and a nonlinear feedback shift register (NFSR) are combined to create a new type of TRNG. This TRNG is based on the intrinsic stochasticity of threshold switching behavior in a Pt/HfO2/TiN memristor and an NFSR circuit. Considering the transition rate of the hopping process, the stochasticity of the delay time can be attributed to the phonon-assisted hopping process. This novel TRNG passes all 15 National Institute of Standards and Technology randomness tests without post-processing steps, proving its performance as a hardware security application. By combining the TRNG with the NFSR, the bit generation rate is further improved, allowing it to be used for high-speed applications.