ABSTRACT. Random number generators are widely used in various fields including encryption, statistical analysis and numerical simulations. They are also a fundamental resource in science and engineering. There are algorithmically generated numbers that look like random numbers but are not truly random, called pseudo random number generators. In cases where true randomness is necessary, we use true random number generators, where unpredictable random events are used as a random source. Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. Our goal is to generate fast random numbers at a lower cost. At the same time, a high level of randomness is essential. It is essential to trust cryptographic random number generators to generate only true random numbers. This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated. We present the improved novel quantum random number generator, which is based the on time of arrival QRNG. It is rather efficient, as it uses the simple version of the detectors with rather few requirements. The novel QRNG produces more than one random bit per each photon detection. Self-testing as well as device independent quantum random number generation methods are analyzed. The advantages and disadvantages of both methods are identified. The model of a novel semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper. This method combines different types of certification approaches and is rather secure and efficient. The paper analyzes its security and efficiency.