We consider the problem of symmetric secret key generation in quasi-static/static environments, where the amount of common randomness obtained from the characteristics of the physical layer channel is limited. In order to provide a high-rate secret key generation mechanism, we introduce a method called induced randomness. In this method, locally generated randomness is assumed at the legitimate parties. Such randomness together with the uniqueness provided by the wireless channel coefficients are utilized to enable high-rate secret key generation. We describe the proposed secret key generation protocol for two scenarios; for the case where the legitimate parties have a direct link (the first scenario), and for the case where the legitimate parties do not have a direct link and communicate through an untrusted relay (the second scenario). After the exchange of the induced randomness, highly correlated samples are generated by the legitimate parties. These samples are then quantized, reconciled, and hashed to compensate for the information leakage to the eavesdropper and to allow verification of consistency of the generated key bit sequences. We utilize semantic security measures and information-theoretic inequalities to upper bound the probability of successful eavesdropping attack in terms of the mutual information measures that can be numerically computed. Given certain reasonable system parameters this bound is numerically evaluated to be 2 −31 and 2 −11.3 in the first and the second scenario, respectively. Furthermore, in the considered numerical setup, the bit generation rate is 64 bits/packet, the bit error rate is 0.002% and 0.0029% in the first and the second scenario, respectively, and the eavesdropper's average bit error rate in both scenarios is almost 50%. The probability of accepting a mismatched key by legitimate parties is also upper bounded using properties of hash functions and is evaluated in the numerical setup to be 0.0015% for both scenarios.
Models trained in machine learning processes may store information about individual samples used in the training process. There are many cases where the impact of an individual sample may need to be deleted and unlearned (i.e., removed) from the model. Retraining the model from scratch after removing a sample from its training set guarantees perfect unlearning, however, it becomes increasingly expensive as the size of training dataset increases. One solution to this issue is utilizing an ensemble learning method that splits the dataset into disjoint shards and assigns them to non-communicating weak learners and then aggregates their models using a pre-defined rule. This framework introduces a trade-off between performance and unlearning cost which may result in an unreasonable performance degradation, especially as the number of shards increases. In this paper, we present a coded learning protocol where the dataset is linearly coded before the learning phase. We also present the corresponding unlearning protocol for the aforementioned coded learning model along with a discussion on the proposed protocol's success in ensuring perfect unlearning. Finally, experimental results show the effectiveness of the coded machine unlearning protocol in terms of performance versus unlearning cost trade-off.INDEX TERMS Machine unlearning, random coding, efficient sample removal.
Cryptographic protocols are often implemented at upper layers of communication networks, while error-correcting codes are employed at the physical layer. In this paper, we consider utilizing readily-available physical layer functions, such as encoders and decoders, together with shared keys to provide a threshold-type security scheme. To this end, the effect of physical layer communication is abstracted out and the channels between the legitimate parties, Alice and Bob, and the eavesdropper Eve are assumed to be noiseless. We introduce a model for threshold-secure coding, where Alice and Bob communicate using a shared key in such a way that Eve does not get any information, in an information-theoretic sense, about the key as well as about any subset of the input symbols of size up to a certain threshold. Then, a framework is provided for constructing threshold-secure codes form linear block codes while characterizing the requirements to satisfy the reliability and security conditions. Moreover, we propose a threshold-secure coding scheme, based on Reed-Muller (RM) codes, that meets security and reliability conditions. Furthermore, it is shown that the encoder and the decoder of the scheme can be implemented efficiently with quasi-linear time complexity. In particular, a low-complexity successive cancellation decoder is shown for the RM-based scheme. Also, the scheme is flexible and can be adapted given any key length.
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