Investigating results and performance of search and construction algorithms for word-based LFSRs, \sigma-LFSRs
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Discrete Applied Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.sciencedirect.com/science/article/pii/S0166218X18300660 |
| Doi | http://dx.doi.org/10.1016/j.dam.2018.01.010 |
| Keywords | Primitive polynomial; LFSR; \sigma-LFSR; Xorshift random number generator |
| Description | Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as \sigma-LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive \sigma-LFSRs. The search algorithm first constructs the \sigma-polynomial and then checks the primitiveness of the \sigma-polynomial, whereas the construction algorithm for the \sigma-LFSR, first finds a primitive polynomial f(x) and then constructs the primitive \sigma-LFSR from f(x). In this paper, we present some novel results pertaining to the search algorithm for primitive \sigma-LFSR along with the exhaustive search space complexity of the search algorithm for \sigma-LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive \sigma-LFSR. Finally, the number of \sigma-LFSRs similar to the \sigma-LFSRs generated by the construction algorithm is provided. |
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