Automatic complexity of shift register sequences

Feedback Shift Register Sequences

Feedback Shift Register (FSR) sequences have been successfully implemented in many communication systems for their randomness properties and ease of implementation. These include ranging and navigation systems, spread spectrum communication systems, CDMA mobile communication systems, and crypto systems such as streamciphers. This article gives a brief overview of FSR sequences, both linear and ...

Algebraic Shift Register Sequences

Pseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions, and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis, and implementation of pseudo-random sequences, particularly those gene...

On Functions of Linear Shift Register Sequences

Linear Filtering of Nonlinear Shift-Register Sequences

Nonlinear n-stage feedback shift-register sequences over the finite field Fq of period q n − 1 are investigated under linear operations on sequences. We prove that all members of an easily described class of linear combinations of shifted versions of these sequences possess useful properties for cryptographic applications: large periods, large linear complexities and good distribution propertie...

Linear Shift-Register Synthesis for Multiple Sequences of Varying Length

The problem of finding the shortest linear shiftregister capable of generating t finite length sequences over some field F is considered. A similar problem was already addressed by Feng and Tzeng. They presented an iterative algorithm for solving this multi-sequence shift-register synthesis problem, which can be considered as generalization of the well known Berlekamp– Massey algorithm. The Fen...