In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register （σ-LFSR） which can make full use of the instructions of modern CPUs so that we can find good σ-LFSR with simple structure and fast software implementation. After analysis, we find a class of simple σ-LFSR with maximal period and give an algorithm of searching for those σ-LFSRs. As a result, we provide a new optional fast component in the design of modern wordbased stream ciphers.
Based on analysis of the structure characteristics and implementation methods of some representative word oriented linear feedback shift registers （LFSRs） in several modem software oriented stream ciphers, this paper firstly classifies the word oriented LFSRs into two classes： the machine instruction type and the arithmetic type. The similarities and differences between each type are illustrated by concrete examples. Then we give a detailed analysis about the word oriented LFSRs in each category from design structure, cryptographic properties and implementation issue aspects. Finally, some basic design criteria for modem word oriented LFSRs and suitable for software implementation are summarized.
