Mutual Relationship between the Neural Network Model and Linear Complexity for Pseudorandom Binary Number Sequence

Machine learning (ML) technology has been getting popular in many applications where ML purposes to analyze or classify data, or predicting the phenomenon follows from the previous conditions, for example. However, the spread of ML technologies allows an attacker to use them into the attack for the sake of sniffing secret information. Since the randomness has been used for an inseparable part of the cryptographic applications to ensure the security, the resistance of a random sequence against analysis based on the ML technologies have to be required. The authors anticipate having the mutual relationship between the classical properties of the randomness, linear complexity (LC) in particular, and the structure of a neural network (NN), which is a class of ML. In this research, the authors find that the strength of each connection between nodes in the NN is relevant to the linear recurrence relation of the target sequence by observing parameters after complete learning. In other words, the difficulty of predicting the next bits from a given sequence would be discussed based on the LC of a sequence in most cases. The experimental results are introduced to clarify the black box in this research.