Biblio
This work deals with key generation based on Physically Obfuscated Keys (POKs), i.e., a certain type of tamper-evident Physical Unclonable Function (PUF) that can be used as protection against invasive physical attacks. To design a protected device, one must take attacks such as probing of data lines or penetration of the physical security boundary into consideration. For the implementation of a POK as a countermeasure, physical properties of a material – which covers all parts to be protected – are measured. After measuring these properties, i.e. analog values, they have to be quantized in order to derive a cryptographic key. This paper will present and discuss the impact of the quantization method with regard to three parameters: key quality, tamper-sensitivity, and reliability. Our contribution is the analysis of two different quantization schemes considering these parameters. Foremost, we propose a new approach to achieve improved tamper-sensitivity in the worst-case with no information leakage. We then analyze a previous solution and compare it to our scenario. Based on empirical data we demonstrate the advantages of our approach. This significantly improves the level of protection of a tamper-resistant cryptographic device compared to cases not benefiting from our scheme.
We investigate the problem of constructing exponentially converging estimates of the state of a continuous-time system from state measurements transmitted via a limited-data-rate communication channel, so that only quantized and sampled measurements of continuous signals are available to the estimator. Following prior work on topological entropy of dynamical systems, we introduce a notion of estimation entropy which captures this data rate in terms of the number of system trajectories that approximate all other trajectories with desired accuracy. We also propose a novel alternative definition of estimation entropy which uses approximating functions that are not necessarily trajectories of the system. We show that the two entropy notions are actually equivalent. We establish an upper bound for the estimation entropy in terms of the sum of the system's Lipschitz constant and the desired convergence rate, multiplied by the system dimension. We propose an iterative procedure that uses quantized and sampled state measurements to generate state estimates that converge to the true state at the desired exponential rate. The average bit rate utilized by this procedure matches the derived upper bound on the estimation entropy. We also show that no other estimator (based on iterative quantized measurements) can perform the same estimation task with bit rates lower than the estimation entropy. Finally, we develop an application of the estimation procedure in determining, from the quantized state measurements, which of two competing models of a dynamical system is the true model. We show that under a mild assumption of exponential separation of the candidate models, detection is always possible in finite time. Our numerical experiments with randomly generated affine dynamical systems suggest that in practice the algorithm always works.