Two new random number generators (RNGs) based on a double-scroll attractor are presented. Simulation and experimental results, verifying the feasibility of the circuits, are given. We have numerically verified that the bit streams, obtained from the 1-dimensional Poincare section of the system, when the map was divided into regions according to distribution, passed the four basic tests of FIPS-140-2 test suite. We have also verified that the binary data, obtained from the hardware realization of the circuit in the same way, passed the full NIST random number test suite. Then, in order to increase the throughput of the generated bit sequences, we have proposed a RNG design which uses a dual oscillator architecture with the chaotic oscillator. Finally, we have experimentally verified that the binary data obtained by this oscillator sampling technique, passed the tests of full NIST random number test suite without post processing for a higher throughput speed. The proposed RNGs can be realized in integrated circuits.