The principle of random selection and the principle of adding biased noise are new paradigms used in several recent papers for constructing lightweight RFID authentication protocols. The cryptographic power of adding biased noise can be characterized by the hardness of the intensively studied Learning Parity with Noise (LPN) Problem. In analogy to this, we identify a corresponding learning problem for random selection and study its complexity. Given
secret linear functions
denotes the problem of learning
, where the secret indices
} and the inputs
are randomly chosen by an oracle. We take an algebraic attack approach to design a nontrivial learning algorithm for this problem, where the running time is dominated by the time needed to solve full-rank systems of linear equations over
unknowns. In addition to the mathematical findings relating correctness and average running time of the suggested algorithm, we also provide an experimental assessment of our results.