Speckle based imaging consists in forming a super-resolved reconstruction of an unknown object from low-resolution images obtained under random inhomogeneous illuminations (speckles). However, the origin of this super-resolution is unclear. In this work, we demonstrate that, under physically realistic conditions, the correlation of the data have a super-resolution power corresponding to the squaring of the imager point spread function. This theoretical result is important for many practical imaging systems such as acoustic and electromagnetic tomographies, fluorescence and photoacoustic microscopies or synthetic aperture radar imaging.