Estimating delay differences of arbiter PUFs using silicon data

This paper presents a novel approach to estimate delay differences of each stage in a standard MUX-based physical unclonable function (PUF). Test data collected from PUFs fabricated using 32 nm process are used to train a linear model. The delay differences of the stages directly correspond to the model parameters. These parameters are trained by using a least mean square (LMS) adaptive algorithm. The accuracy of the response using the proposed model is around 97.5% and 99.5% for two different PUFs. Second, the PUF is also modeled by a perceptron. The perceptron has almost 100% classification accuracy. A comparison shows that the perceptron model parameters are scaled versions of the model derived by the LMS algorithm. Thus, the delay differences can be estimated from the perceptron model where the scaling factor is computed by comparing the models of the LMS algorithm and the perceptron. Because the delay differences are challenge independent, these parameters can be stored on the server. This will enable the server to issue random challenges whose responses need not be stored. An analysis of the proposed model confirms that the delay differences of all stages of the PUFs on the same chip belong to the same Gaussian probability density function.