  In cryptanalysis, security of ciphers vis-a-vis attacks is gauged against
three criteria of complexities, i.e., computations, memory and time. Some
features may not be so apparent in a particular domain, and their analysis in a
transformed domain often reveals interesting patterns. Moreover, the complexity
criteria in different domains are different and performance improvements are
often achieved by transforming the problem in an alternate domain. Owing to the
results of coding theory and signal processing, Discrete Fourier Transform
(DFT) based attacks have proven to be efficient than algebraic attacks in terms
of their computational complexity. Motivated by DFT based attacks, we present a
transform domain analysis of Linear Feedback Shift Register(LFSR) based
sequence generators. The time and frequency domain behavior of non-linear
filter and combiner generators is discussed along with some novel observations
based on the Chinese Remainder Theorem (CRT). CRT is exploited to establish
patterns in LFSR sequences and underlying cyclic structures of finite fields.
Application of DFT spectra attacks on combiner generators is also demonstrated.
Our proposed method saves on the last stage computations of selective DFT
attacks for combiner generators. The proposed approach is demonstrated on some
examples of combiner generators and is scalable to general configuration of
combiner generators.
