Federated learning (FL) faces many security threats. Although multiple robust FL frameworks have been proposed to defend against these malicious attacks in horizontal federated learning (HFL), security issues in vertical federated learning (VFL) have not been adequately studied. Recent studies show that VFL is vulnerable to inference attacks (e.g., label inference attacks), which puts VFL at risk. To solve this problem, we propose a new VFL framework SVFL (Secure Vertical Federated Learning) to defend against privacy breaches inspired by feature disentanglement. Specifically, in SVFL , the bottom models are feature extractors to extract samples’ features in the high-dimensional space, and the top model sews samples’ features of the same sample ID. Then, disentangling the samples’ features into the class-relevant feature and class-irrelevant one via two classifiers: one is to recognize the class-relevant feature by regular training, and another is to recognize the class-irrelevant feature by adversarial training . Our experiments show that SVFL not only defends against label inference attacks, no matter how many samples features a malicious participant occupies, but also improves the global model’s accuracy. Therefore, SVFL provides a privacy security guarantee for the vertical federated learning system .

Based on the trace representation of Boolean functions, we devise an evolutionary algorithm to design bent functions. Using this algorithm, we then construct many bent functions and perform some analyses. First, we observe that each of the four affinely inequivalent bent functions in six variables can be written as the linear sum of two or three monomial trace functions. We draw the conclusion that the affine transformation can be used to change the linear span of the Boolean functions and thereby change the trace representation of our obtained bent functions. Second, we find that certain exponents are more suitable for constructing bent functions than others. From this observation, we assign each exponent a cost function, which makes our algorithm more efficient than an exhaustive search algorithm or a random algorithm. Third, we classify the obtained bent functions into affinely inequivalent classes, and the number of classes is presented.