## 1 Introduction  
At present, password-based identity authentication is one of the most popular authentication methods; however, the use of passwords is not always secure. Generally, people are used to setting short passwords or character sequences that are easy to remember [1, 2], such as \"123456\". In addition, due to the endowment effect [3], even people with high-security Markov awareness still use weak passwords. In this regard, many researchers have proposed password setting strategies [4, 5, 6, 7, 8] to help users set passwords that are easy to remember but difficult to guess.  
Research on password strategy and password security, such as detecting the defects of existing user password-protection mechanisms, requires large-scale password plaintext samples. However, it is difficult to completely describe the real-world password plaintext situation accurately. Therefore, password-generation technology to generate large-scale password sets is currently a widely-applied method.  
In the available studies [9, 10], a situation can be observed where models based on statistical methods can generate a password set according to the usage probability of passwords and place the more commonly-used passwords at the front to speed up password cracking, which does not accurately reflect the distribution feature of the original password set when the generated quantity is large.  
Although models based on neural networks can accurately reflect the distribution characteristics of the original password set, the performance of the password generator decreases with the increase of training rounds [11], which means that the repetition rate of passwords becomes higher. These two types of situations will reduce the quality of the password set and further reduce the efficiency of password cracking engineering. In particular, it is observed that the advantages of these two types of models are complementary.  
Aiming at the above-mentioned problems, we considered that, if two models with different characteristics can be integrated, the impacts of these shortcomings will be weakened or even eliminated, which means the password-generation model itself will be greatly improved. Accordingly, a password-generation model based on as ordered Markov enumerator and critic discriminant network (OMECDN) is proposed, where passwords are generated via an ordered Markov enumerator (OMEN) and a discriminant network according to the probability of the combination of passwords. First, the OMEN model generates a password set. Passwords are combined, scored, and filtered by a discriminative neural network. Then, the final password set is formed by the selected passwords with a higher score than a preset threshold.  
For instance, in the case of the generation of \(10^{7}\) passwords, the matching entries of the password set generated by the OMECDN model on the RockYou dataset were 25.18% higher than those of the OMEN model and 243.58% higher than those of the PassGAN model, respectively. The main work and contributions are as follows:  
1. A password generation selection model is proposed, which is based on an ordered Markov enumerator and a critic discriminant network. Accordingly, the password set generated by this model has features of both the above methods: it can be ranked according to the password combination probability, and it can match the password distribution of the real password set.
2. Compared with the existing GAN-based methods, OMECDN sorts according to the probability of password combination, which can remedy the problem of the repetition rate.
3. Experimental results show that OMECDN achieved a qualitative improvement in hit rate metrics compared to its base model.