Abstract
The word-based LFSRs called σ-LFSRs are very attractive as they take advantage of the modern word-based processor and thus increase the throughput. Secondly, the bitstream produced by σ-LFSR has excellent statistical properties with a high period except for low linear complexity. In order to increase the linear complexity, the concept of both bit-oriented shrinking and self-shrinking generators is introduced in case of σ-LFSRs. In both the cases, the lower bound for the period as well as for the linear complexity of the bitstream are shown to be exponential. Further, we have experimented and investigated more results on the periodicity and statistical properties of the bitstream in self-shrinking σ-LFSRs. This helps to find and prove the exact period of the bitstream produced by self-shrinking generators.
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