A rapid and low-cost method to sequence DNA would usher in a revolution in medicine. We propose and theoretically show the feasibility of a protocol for sequencing based on the distributions of transverse electrical currents of single-stranded DNA while it translocates through a nanopore. Our estimates, based on the statistics of these distributions, reveal that sequencing of an entire human genome could be done with very high accuracy in a matter of hours without parallelization, e.g., orders of magnitude faster than present techniques. The practical implementation of our approach would represent a substantial advancement in our ability to study, predict and cure diseases from the perspective of the genetic makeup of each individual.