For cryptography and secure communications, it is very prerequisite that the ran- dom number generator (RNG) is based on non-deterministic physical mechanisms, extremely fast generator and robustness to noise are required. In this work, we present novel fast optoelectronic architecture RNGs based on integer domain chaotic iteration (IDCI), with a chaotic semiconduc- tor laser, having time-delayed self-feedback. The solution stems from some well-defined discrete chaotic iterations that satisfy the reputed Devaney’s definition of chaos, namely the integer do- main chaotic iterations technique, improve the statistical properties of this RNG. Using standard criteria named NIST and DieHARD (famous batteries of tests), the randomness of the output sequences is verified.