In password guessing, the Markov model is still widely used due to its simple structure and fast inference speed. However, the Markov model based on random sampling to generate passwords has the problem of a high repetition rate, which leads to a low cover rate. The model based on enumeration has a lower cover rate for high-probability passwords, and it is a deterministic algorithm that always generates the same passwords in the same order, making it vulnerable to attack. We design a dynamic distribution mechanism based on the random sampling method. This mechanism enables the probability distribution of passwords to be dynamically adjusted and tend toward uniform distribution strictly during the generation process. We apply the dynamic distribution mechanism to the Markov model and propose a dynamic Markov model. Through comparative experiments on the RockYou dataset, we set the optimal adjustment degree $\alpha$. Compared with the Markov model without the dynamic distribution mechanism, the dynamic Markov model reduced the repetition rate from 75.88% to 66.50% and increased the cover rate from 37.65% to 43.49%. In addition, the dynamic Markov model had the highest cover rate for high-probability passwords. Finally, the model avoided the lack of a deterministic algorithm, and when it was run five times, it reached almost the same cover rate as OMEN.

With the development of the Internet, information security has attracted more attention. Identity authentication based on password authentication is the first line of defense; however, the password-generation model is widely used in offline password attacks and password strength evaluation. In real attack scenarios, high-probability passwords are easy to enumerate; extremely low-probability passwords usually lack semantic structure and, so, are tough to crack by applying statistical laws in machine learning models, but these passwords with lower probability have a large search space and certain semantic information. Improving the low-probability password hit rate in this interval is of great significance for improving the efficiency of offline attacks. However, obtaining a low-probability password is difficult under the current password-generation model. To solve this problem, we propose a low-probability generator–probabilistic context-free grammar (LPG–PCFG) based on PCFG. LPG–PCFG directionally increases the probability of low-probability passwords in the models’ distribution, which is designed to obtain a degeneration distribution that is friendly for generating low-probability passwords. By using the control variable method to fine-tune the degeneration of LPG–PCFG, we obtained the optimal combination of degeneration parameters. Compared with the non-degeneration PCFG model, LPG–PCFG generates a larger number of hits. When generating ${10}^7$ and ${10}^8$ times, the number of hits to low-probability passwords increases by $50.4\%$ and $42.0\%$, respectively.

In a satellite-denied environment, a swarm of drones is capable of achieving relative positioning and navigation by leveraging the high-precision ranging capabilities of the inter-drone data link. However, because of factors such as high drone mobility, complex and time-varying channel environments, electromagnetic interference, and poor communication link quality, distance errors and even missing distance values between some nodes are inevitable. To address these issues, this paper proposes a low-rank optimization algorithm based on the eigenvalue scaling of the distance matrix. By gradually limiting the eigenvalues of the observed distance matrix, the algorithm reduces the rank of the matrix, bringing the observed distance matrix closer to the true value without errors or missing data. This process filters out distance errors, estimates and completes missing distance elements, and ensures high-precision calculations for subsequent topology perception and relative positioning. Simulation experiments demonstrate that the algorithm exhibits significant error filtering and missing element completion capabilities. Using the F-norm metric to measure the relative deviation from the true value, the algorithm can optimize the relative deviation of the observed distance matrix from 11.18% to 0.25%. Simultaneously, it reduces the relative positioning error from 518.05 m to 35.24 m, achieving robust topology perception and relative positioning for the drone swarm formation.

In military operational environments, satellite navigation is typically unavailable, and unmanned aerial vehicle swarms must rely on inter-node communication links for distance measurement to achieve relative positioning. When the absolute positions of a subset of nodes are known, this approach can also enable absolute positioning of the entire swarm. Conventional relative positioning methods often overlook the inherent difference in ranging ability, assuming the same distance errors across all nodes. This oversimplification leads to significant positioning inaccuracies and slow convergence. To address these limitations, this paper proposes a distance error variance adjustable relative positioning method, DEVARP. The proposed method assigns varying confidence weights to inter-node distance measurements based on link quality, and solves it by continuous numerical iteration so as to achieve high-speed and high-precision positioning. In the simulation experiments involving a 32-node UAV swarm, the results show that the confidence-adjustable method achieves an absolute positioning error below 1 m with a probability of 91.05%, compared to 76.57% for traditional methods—a 14.48% improvement. Additionally, the proposed method converges within seven iterations with a probability of 94.10%. In contrast, conventional methods achieve the same result in seven steps with a probability of 78.83% —a 17.53% performance gap—which confirms both the accuracy and computational efficiency of the method.