Data security is a vital concern in modern computing. At the same time, in the aspiration to overcome the von-Neumann bottleneck, a rising variety of resistive random access memory (RRAM) devices are being integrated particularly in memory units. Combining these two developments, two approaches to generate true random numbers from read noise measured on redox-based RRAM (ReRAM) are presented. It is shown that true random numbers can be generated from read noise in a single-step process by utilizing the time increment of the signal. However, this approach is limited by the sampling rate and physical processes like the motion of oxygen vacancies. Additionally, the random numbers are predictable if the read noise itself is known, as no additional keys exist. Therefore, a second approach is presented in which the read noise is used as a seed for a 4-bit Fibonacci Non-Linear Feedback Shift Register. The generator increases the data generation rate and yields additional keys preventing the prediction of the random number. The proposed design allows for time and hardwareefficient generation of true random numbers. Both sets of generated random numbers pass bench marking requirements for random numbers set by the National Institute of Standards and Technology (NIST). The read noise is measured on filamentary valence change mechanism (VCM) based ReRAM devices.