With the massive amounts of data generated by Industrial Internet of Things (IIoT) devices at all moments, federated learning (FL) enables these distributed distrusted devices to collaborate to build machine learning model while maintaining data privacy. However, malicious participants still launch malicious attacks against the security vulnerabilities during model aggregation. This paper is the first to propose sybil-based collusion attacks (SCA) in the IIoT-FL system for the vulnerabilities mentioned above. The malicious participants use label flipping attacks to complete local poisoning training. Meanwhile, they can virtualize multiple sybil nodes to make the local poisoning models aggregated with the greatest possibility during aggregation. They focus on making the joint model misclassify the selected attack class samples during the testing phase, while other non-attack classes kept the main task accuracy similar to the non-poisoned state. Exhaustive experimental analysis demonstrates that our SCA has superior performance on multiple aspects than the state-of-the-art.

Federated learning (FL) enables a great deal of distributed independent participants to collaborate in training without sharing data. Malicious adversary can poison the local model by backdoor poisoning attacks and utilize the characteristic that server cannot trace original data to make the poisoned model directly aggregated. Especially in the AIoT-FL network that generates large amounts of data in real-time, such an attack is more powerful. In this paper, we design a sybil-based backdoor poisoning attacks (SBPA) against the above vulnerability. Malicious participants inject backdoor triggers into distributed Big Data to covertly complete data poisoning. During subsequent iterative aggregation, the joint model activates the backdoor during testing to achieve misclassification for the backdoor images. Besides, malicious participants create some sybil nodes to join the aggregation by taking advantage of the vulnerability of system devices to be easily disconnected. They are committed to making the poisoned local models aggregated with higher probability. Their goal works on making the final global model misclassify backdoor images while keeping high classification accuracy on the other non-backdoor samples. We conduct extensive experiments on multiple datasets and exhibit more robust performance than the state-of-the-art in various metrics under both data distribution including i.i.d. and non-i.i.d. scenarios.

The Horner and Goertzel algorithms are frequently used in polynomial evaluation. Each of them can be less expensive than the other in special cases. In this paper, we present a new compensated algorithm to improve the accuracy of the Goertzel algorithm by using error-free transformations. We derive the forward round-off error bound for our algorithm, which implies that our algorithm yields a full precision accuracy for polynomials that are not too ill-conditioned. A dynamic error estimate in our algorithm is also presented by running round-off error analysis. Moreover, we show the cases in which our algorithms are less expensive than the compensated Horner algorithm for evaluating polynomials. Numerical experiments indicate that our algorithms run faster than the compensated Horner algorithm in those cases while producing the same accurate results, and our algorithm is absolutely stable when the condition number is smaller than ${10}^{16}$. An application is given to illustrate that our algorithm is more accurate than MATLAB’s $\mathtt{fft}$ function. The results show that the relative error of our algorithm is from ${10}^{15}$ to ${10}^{17}$, and that of the $\mathtt{fft}$ was from ${10}^{12}$ to ${10}^{15}$.