On the linear complexity of feedforward clock-controlled sequence

TL;DR

This paper develops a new method using matrix theory to estimate the lower bound of linear complexity in feedforward clock-controlled sequences, enhancing understanding of their security properties beyond m-sequences.

Contribution

It introduces a matrix-based approach to estimate the lower bound of linear complexity for feedforward clock-controlled sequences, applicable even when the controlled sequence is not an m-sequence.

Findings

The method provides a useful estimate of linear complexity lower bounds.

It applies to sequences with high linear complexity.

The approach extends previous results limited to m-sequences.

Abstract

As a research field of stream ciphers, the pursuit of a balance of security and practicality is the focus. The conditions for security usually have to satisfy at least high period and high linear complexity. Because the feedforward clock-controlled structure can provide quite a high period and utility, many sequence ciphers are constructed based on this structure. However, the past study of its linear complexity only works when the controlled sequence is an m-sequence. Using the theory of matrix over the ring and block matrix in this paper, we construct a more helpful method. It can estimate the lower bound of the linear complexity of the feedforward clock-controlled sequence. Even the controlled sequence has great linear complexity.