Two random number generation methods based on a double-scroll chaotic system are introduced. Numerical models for the proposed designs have been developed where bootstrap method is utilized which allows us to estimate the statistical characteristics of underlying chaotic signals. Offset compensation loops have been developed in order to maximize the statistical quality of the output sequence and to be robust against external interference and parameter variations. Numerical results, verifying the feasibilities and correct operations of the random number generators are given such that numerically generated binary sequences fulfill FIPS-140-2 statistical test suites for randomness without post-processing.