Electron diffractive imaging (EDI) relies on combining information from the high-resolution transmission electron microscopy image of an isolated kinematically diffracting nano-particle with the corresponding nano-electron diffraction pattern. Phase-retrieval algorithms allow one to derive the phase, lost in the acquisition of the diffraction pattern, to visualize the actual atomic projected potential within the specimen at sub-ångström resolution, overcoming limitations due to the electron lens aberrations. Here the approach is generalized to study extended crystalline specimens. The new technique has been called keyhole electron diffractive imaging (KEDI) because it aims to investigate nano-regions of extended specimens at sub-ångström resolution by properly confining the illuminated area. Some basic issues of retrieving phase information from the EDI/KEDI measured diffracted amplitudes are discussed. By using the generalized Shannon sampling theorem it is shown that whenever suitable oversampling conditions are satisfied, EDI/KEDI diffraction patterns can contain enough information to lead to reliable phase retrieval of the unknown specimen electrostatic potential. Hence, the KEDI method has been demonstrated by simulations and experiments performed on an Si crystal cross section in the [112] zone-axis orientation, achieving a resolution of 71 pm.