Gao Ming

Gao Ming

P vs NP problem is the most important unresolved problem in the field of computational complexity. Its impact has penetrated into all aspects of algorithm design, especially in the field of cryptography. The security of cryptographic algorithms based on short keys depends on whether P is equal to NP. In fact, the security requirements for cryptographic keys are much stricter than those for P$\neq$NP, the security of the key must ensure not only a sufficiently high computational complexity to crack it, but also consider the security of each bit of the key, while fully avoiding the effectiveness of various attack methods. In this paper, we innovatively propose a new encoding mechanism and develop a novel block symmetric encryption algorithm, whose encryption and decryption can be completed in linear time. For the attacker, in the case where only the plaintext-ciphertext correspondence is known, the problem of cracking the key is equivalent to solving a system of equations which contains at least one free variable that cannot be eliminated, and the number of possible values for each variable is exponentially to the length of the key. To solve this system of equations, it is necessary to exhaustively search for at least one variable, thus proving that the computational complexity of cracking the key is exponential. So the decryption is a one-way function, and according to "the existence of one-way function means P$\neq$NP", thus solving the unsolved problem of P vs NP. In addition, this paper delves into the underlying mathematical laws of this new encoding mechanism, and develops a right multiplication operation to binary. Based on this right multiplication operation, we further constructed a nonlinear operation and designed another block symmetric encryption algorithm that is resistant to all forms of linear and differential attacks.

Li Kai, Li Ning, Zhang Wei et al.

Based on the traditional VAE, a novel neural network model is presented, with the latest molecular representation, SELFIES, to improve the effect of generating new molecules. In this model, multi-layer convolutional network and Fisher information are added to the original encoding layer to learn the data characteristics and guide the encoding process, which makes the features of the data hiding layer more aggregated, and integrates the Long Short Term Memory neural network (LSTM) into the decoding layer for better data generation, which effectively solves the degradation phenomenon generated by the encoding layer and decoding layer of the original VAE model. Through experiments on zinc molecular data sets, it is found that the similarity in the new VAE is 8.47% higher than that of the original ones. SELFIES are better at generating a variety of molecules than the traditional molecular representation, SELFIES. Experiments have shown that using SELFIES and the new VAE model presented in this paper can improve the effectiveness of generating new molecules.