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The Italian Institute of Nuclear Physics (INFN) is involved in the development of a demonstrator for a SiPM-based camera for the Cherenkov Telescope Array (CTA) experiment, with a pixel size of 6$\times$6 mm$^2$. The camera houses about two thousands electronics channels and is both light and compact. In this framework, a R&D program for the development of SiPMs suitable for Cherenkov light detection (so called NUV SiPMs) is ongoing. Different photosensors have been produced at Fondazione Bruno Kessler (FBK), with different micro-cell dimensions and fill factors, in different geometrical arrangements. At the same time, INFN is developing front-end electronics based on the waveform sampling technique optimized for the new NUV SiPM. Measurements on 1$\times$1 mm$^2$, 3$\times$3 mm$^2$, and 6$\times$6 mm$^2$ NUV SiPMs coupled to the front-end electronics are presented