We present a computationally efficient technique to build concise and accurate computational models for large (60 or more inputs, 1 output) Boolean functions, only a very small fraction of whose truth table is known during model building. We use Genetic Programming with Boolean logic operators, and enhance the accuracy of the technique using Reduced Ordered Binary Decision Diagram based representations of Boolean functions, whereby we exploit their canonical forms. We demonstrate the effectiveness of the proposed technique by successfully modeling several common Boolean functions, and ultimately by accurately modeling a 63-input Physically Unclonable Function circuit design on Xilinx Field Programmable Gate Array. We achieve better accuracy (at lesser computational overhead) in predicting truth table entries not seen during model building, than a previously proposed machine learning based modeling technique for similar Physically Unclonable Function circuits using Support Vector Machines. The success of this modeling technique has important implications in determining the acceptability of Physically Unclonable Functions as useful hardware security primitives, in applications such as anti-counterfeiting of integrated circuits.