A system and method for generation of unpredictable and auditable random numbers includes a host computer, a digital signature server and a verification device. The host computer provides data to the digital signature server; obtains digital signature for this data; uses elements of this signature for random numbers generation; logs relevant data for audit. The verification device uses logged data for auditing of the random number generation process. This invention can be applied in gaming and gambling industries where the random numbers are used for generation of game/play elements and of winning numbers elements. The game/play elements and winning numbers elements generated using this invention can be audited.