Now showing 1 - 2 of 2
ItemOn Privacy of Quantized Sensor Measurements through Additive NoiseMurguia, C ; Shames, I ; Farokhi, F ; Nesic, D ( 2018-09-10)We study the problem of maximizing privacy of quantized sensor measurements by adding random variables. In particular, we consider the setting where information about the state of a process is obtained using noisy sensor measurements. This information is quantized and sent to a remote station through an unsecured communication network. It is desired to keep the state of the process private; however, because the network is not secure, adversaries might have access to sensor information, which could be used to estimate the process state. To avoid an accurate state estimation, we add random numbers to the quantized sensor measurements and send the sum to the remote station instead. The distribution of these random variables is designed to minimize the mutual information between the sum and the quantized sensor measurements for a desired level of distortion -- how different the sum and the quantized sensor measurements are allowed to be. Simulations are presented to illustrate our results.
ItemInformation-Theoretic Privacy through Chaos Synchronization and Optimal Additive NoiseMurguia, C ; Shames, I ; Farokhi, F ; Nesic, D ( 2019-06-03)We study the problem of maximizing privacy of data sets by adding random vectors generated via synchronized chaotic oscillators. In particular, we consider the setup where information about data sets, queries, is sent through public (unsecured) communication channels to a remote station. To hide private features (specific entries) within the data set, we corrupt the response to queries by adding random vectors. We send the distorted query (the sum of the requested query and the random vector) through the public channel. The distribution of the additive random vector is designed to minimize the mutual information (our privacy metric) between private entries of the data set and the distorted query. We cast the synthesis of this distribution as a convex program in the probabilities of the additive random vector. Once we have the optimal distribution, we propose an algorithm to generate pseudorandom realizations from this distribution using trajectories of a chaotic oscillator. At the other end of the channel, we have a second chaotic oscillator, which we use to generate realizations from the same distribution. Note that if we obtain the same realizations on both sides of the channel, we can simply subtract the realization from the distorted query to recover the requested query. To generate equal realizations, we need the two chaotic oscillators to be synchronized, i.e., we need them to generate exactly the same trajectories on both sides of the channel synchronously in time. We force the two chaotic oscillators into exponential synchronization using a driving signal. Exponential synchronization implies that trajectories of the oscillators converge to each other exponentially fast for all admissible initial conditions and are perfectly synchronized in the limit only. Thus, in finite time, there is always a “small” difference between their trajectories. To implement our algorithm, we assume (as it is often done in related work) that systems have been operating for sufficiently long time so that this small difference is negligible and oscillators are practically synchronized. We quantify the worst-case distortion induced by assuming perfect synchronization, and show that this distortion vanishes exponentially fast. Simulations are presented to illustrate our results.