Vectorial Feedback with Carry Registers and Memory requirements

TL;DR

This paper introduces the Ring mode for vectorial Feedback with Carry Shift Registers (FCSRs), providing analysis methods and examples, expanding the understanding of their structure and potential applications in cryptography.

Contribution

It extends the vectorial conception of FCSRs by defining and analyzing the Ring mode, complementing previous Fibonacci and Galois modes.

Findings

Introduction of the Ring mode for vectorial FCSRs

Analysis methods for the Ring mode

Illustrative example demonstrating the mode

Abstract

In \cite{marjane2010}, we have introduced vectorial conception of FCSR's in Fibonacci mode. This conception allows us to easily analyze FCSR's over binary finite fields $\mathbb{F}_{2^{n}}$ for $n\geq 2$. In \cite{allailou2010}, we describe and study the corresponding Galois mode and use it to design a new stream cipher. In this paper, we introduce the Ring mode for vectorial FCSR, explain the analysis of such Feedback registers and illustrate with a simple example.