We have developed a methodology for unique identification of integrated circuits (ICs) that addresses untrusted fabrication and other security problems. The new method leverages nondestructive gate-level characterization of ICs post-manufacturing, revealing the hidden and unclonable uniqueness of each IC. The IC characterization uses the externally measured leakage currents for multiple input vectors. We have derived several optimization techniques for gate-level characterization. The probability of collision of IDs in presence of intra- and inter-chip correlations is computed. We also introduce a number of novel security and authentication protocols, such as hardware metering, challenge-based authentication and prevention of software piracy, that leverage the extraction of a unique ID for each IC. Experimental evaluations of the proposed approach on a large set of benchmark examples reveals its effectiveness even in presence of measurement errors.