ASTRI SST-2M is an Imaging Atmospheric Cherenkov Telescope (IACT) developed by the Italian National Institute of Astrophysics, INAF. It is the prototype of the ASTRI telescopes proposed to be installed at the southern site of the Cherenkov Telescope Array, CTA. The optical system of the ASTRI telescopes is based on a dual mirror configuration, an innovative solution for IACTs, and the focal plane of the camera is composed of silicon photo-multipliers (SiPM), a recently developed technology for light detection, that exhibit very fast response and an excellent single photoelectron resolution. The ASTRI camera electronics is specifically designed to directly interface the SiPM sensors, detecting the fast pulses produced by the Cherenkov flashes, managing the trigger generation, the digital conversion of the signals and the transmission of the data to an external camera server connected through a LAN. In this contribution we present the general architecture of the camera electronics developed for the ASTRI SST-2M prototype, with special emphasis to some innovative solutions.