CRT and Fixed Patterns in Combinatorial Sequences
This work addresses structural analysis challenges for researchers in cryptography and coding theory, representing an incremental advancement in combinatorial sequence analysis.
The paper tackles the problem of analyzing combinatorial sequence generators by applying the Chinese Remainder Theorem to identify fixed patterns in LFSR sequences and cyclic structures in finite fields, introducing a new method for computing DFT spectral points in higher fields from smaller ones, and demonstrating this approach on combiner generators with scalability to general configurations.
In this paper, new context of Chinese Remainder Theorem (CRT) based analysis of combinatorial sequence generators has been presented. CRT is exploited to establish fixed patterns in LFSR sequences and underlying cyclic structures of finite fields. New methodology of direct computations of DFT spectral points in higher finite fields from known DFT spectra points of smaller constituent fields is also introduced. Novel approach of CRT based structural analysis of LFSR based combinatorial sequence is given both in time and frequency domain. The proposed approach is demonstrated on some examples of combiner generators and is scalable to general configuration of combiner generators.