Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.