A New-Type Zeroing Neural Network Model and Its Application in Dynamic Cryptography

Cryptography is the core of information security. Among various types of ciphers, the traditional Hill Cipher (THC) is a static alternative cipher based on the basic matrix theory. Stuck in the security and real-time issues of the THC with time-invariant key, this paper studies a dynamic novel Hill Cipher (NHC) with time-variant key for the first time. To ensure the fast decryption of the NHC, this work chooses the zeroing neural network (ZNN) which plays vital important role in solving dynamic problems as the decryption algorithm of NHC to solve the time-variant key inversion (TVKI) matrix. Specifically, a new robust fixed-time convergent activation function (NRFT-AF) and a new time-variant convergence factor (NTv-CF) are designed, and thus a new-type zeroing neural network model (NT-ZNN) is constructed by them for solving the TVKI. By virtue of abundant rigorous mathematical derivation, the fixed-time convergence and robustness of NT-ZNN model for solving the TVKI under the cases without noise and with noise are theoretically demonstrated in detail. Moreover, the NHC is also applied to the encryption and decryption experiments of different strings and RGB color image to validate its reliability. Then, comparative simulation results of the NT-ZNN model with conventional-type zeroing neural network (CT-ZNN) models constructed by other existing activation functions (AFs) and convergence factors (CFs) for solving the TVKI are given, and the superiority of the NT-ZNN model in NHC decryption is further verified.