Time of flight (TOF) measurements in positron emission tomography (PET) are very challenging in terms of timing performance, and should ideally achieve less than 100 ps FWHM precision. We present a time-based differential technique to read out silicon photomultipliers (SiPMs) which has less than 20 ps FWHM electronic jitter. The novel readout is a fast front end circuit (NINO) based on a first stage differential current mode amplifier with 20 Ω input resistance. Therefore the amplifier inputs are connected differentially to the SiPM's anode and cathode ports. The leading edge of the output signal provides the time information, while the trailing edge provides the energy information. Based on a Monte Carlo photon-generation model, HSPICE simulations were run with a 3 × 3 mm2 SiPM-model, read out with a differential current amplifier. The results of these simulations are presented here and compared with experimental data obtained with a 3 × 3 × 15 mm3 LSO crystal coupled to a SiPM. The measured time coincidence precision and the limitations in the overall timing accuracy are interpreted using Monte Carlo/SPICE simulation, Poisson statistics, and geometric effects of the crystal.