On Parallel Generation of Linear Recurring Sequences
Joven Dj Golic · International Symposium on Information Theory and its Applications · 1994
A novel, simple and compact approach to deriving the minimum generating polynomial of decimated linear recurring finite field sequences is developed. The minimum polynomial of the set of d sequences obtained from the decimation by d of d successive phase shifts of an arbitrary linear recurring finite field sequence is thus determined. This is interesting for high speed parallel generation of linear feedback shift register sequences. Necessary and sufficient conditions for the linear complexity of a decimated sequence to be the same as for the original sequence are also obtained. This may be useful in cryptographic applications for analysing the algebraic properties of shift register based key stream generators.